At a point A(1, 1) on ellipse, equation of tangent is y = x. If one of the foci of ellipse is (0, -2) and the co-ordinates of center of ellipse are (a, b) then the value of a + b is (Given length of major axis of ellipse is 4√10 units) At a point A(1, 1) on ellipse, equation oftangent is y = x. If one of the foci of ellipseis (0, -2) and the co-ordinates of center ofellipse are (a, B) then the value of a + B is(Given length of major axis of ellipse is 410 units)%3D

Answered: Image /qna-images/answer/bf223a0f-ff7d-47a6-b116-1cb282dc4c5c.jpg

At a point A(1, 1) on ellipse, equation of tangent is y = x. If one of the foci of ellipse is (0, -2) and the co-ordinates of center of ellipse are (a, B) then the value of a + B is (Given length of major axis of ellipse is 4 10 units) %3D

At a point A(1, 1) on ellipse, equation of tangent is y = x. If one of the foci of ellipse is (0, -2) and the co-ordinates of center of ellipse are (a, B) then the value of a + B is (Given length of major axis of ellipse is 4 10 units) %3D

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.2: Ellipses

Problem 35E

See similar textbooks

Related questions

Q: A line segment of length a + b runs from the x-axis to the y-axis. The point P on the segment lies a…

A: Given A line segment of length a + b runs from the x-axis to the y-axis. The point P on the segment…

Q: 4. The upper half of the ellipse centered at the origin with axes of length 2a and 2b is described…

Q: 7. The arch of an underpass is a semi-ellipse 20 meters wide and 5 meters high. Find the clearance…

Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. Use Lagrange…

A: Note that here we have to extremize x2+y2+z2 , whch is eqivalently ,to extrimize x2+y2+z2.

Q: Let S be the quadric with equation 36x² – 4y² – 9z2 – 36x = 0 • Classify the graph of S…

A: Given, S is the quadric with the equation 36x2-4y2-9z2-36x=0

Q: In some designs of eyeglasses, the surface is "aspheric," meaning that the contour varies slightly…

Q: The plane x+ y+2z =2 intersects the paraboloid z = x2+y² in an ellipse. Find the points on this…

A: Given a plane x+y+2z=2 intersects the paraboloid z=x2+y2 in an ellipse We need to find the points on…

Q: 11. A rectangle of maximum perimeter is to be inscibed in the ellipse x^2/24^2 + y^2/13^2 = 1. The…

Q: Determine the eccentricity of a hyperbola with a vertical transverse axis of length 48 units and…

Q: Two friends visit a whispering gallery (in the shape of a semi-ellipsoid) where they stand 100 m…

A: Given: Two friends are standing in a semi ellipsoid gallery at 100 apart at foci. So let's take the…

Q: An arch is in the form of a semi-ellipse that has a span of 250 ft and with the greatest height of…

A: The equation of an ellipse is x2a2+y2b2=1. Here, 2a is the length of the major axis, and 2b is the…

Q: ind the points on the ellipse 5x2 + y2 = 5 that are farthest away from the point (1, 0). smaller…

Q: Find an equation of the hyperbola that has foci at (-15, 0) and (15, 0), and asymptotes y= x and y=

Q: Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0). (x,y)=(?)…

Q: center, horizontally, is the car when it is at an altituue Ul 23 IL! 2. A truck has to pass under an…

Q: Find the locus of the foot of the perpendicular from the center of the ellipse x²/a²+y²/b² = 1 on…

A: Let end points of chord be P(acosθ,bsinθ) and Q(acosθ-π2,bsinθ-π2)that is P(acosθ,bsinθ) and…

Q: Find the area of the resulting surface if an arc of a parabola y=x2 from (1,1) to (2,4) is rotated…

Q: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

A: Given information: The cables touch the road surface at the center of the bridge, Then image a graph…

Q: Find an equation of the ellipse with foci at (−3,7)and (−3,−3) and whose major axis has length 20.…

A: The foci of the ellipse is (−3,7)and (−3,−3). The length of the major axis is 20.

Q: What are the lengths of the major and minor axes of this ellipse 6 =D1? O Major Axis: 6 units, Minor…

Q: A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/20^2 + y^2/12^2 = 1. The…

Q: 3) A large racetrack can be modeled by the ellipse x2 + = 1, where x and y are measured in…

A: An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the…

Q: The reflector of a searchlight is in the shape of a paraboloid of revolution. Its diameter is 16…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/22^2 + y^2/10^2 = 1. The…

Q: Determine the area of the largest circle that can be enclosed by the two hyperbolae, xy= 1 and xy =…

A: Solution is here

Q: 3) Find the family of curve that intersects the family of hyperbolas y = 2r+b at an angle arctan(1)…

A: Given the equation of family of hyperbolas is y2=2x2+b

Q: 7. Find an equation in standard form for the ellipse with center at (5,7), horizontal major axis of…

Q: 29. A tank full of water has the shape of a paraboloid of revolu. tion as shown in the figure; that…

A: Height is 4 feet and radius at the top is 4 feet So the parabola passes through the point (4,4) The…

Q: A line tangent to the hyperbola 4x² −y² = 36 intersects the y-axis at the point (0, 4). Find the…

A: Consider the given hyperbola 4x2-y2=36 Let the point Pα, β be on the the hyperbola. To find the…

Q: Find the points on the ellipse 3x2 + y2 = 3 that are farthest away from the point (1, 0). What I…

Q: 5. An elliptic cone with an ellipse trace parallel to yz-plane, A. Has a hyperbola trace in both xz-…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. What is the point on…

A: We will use Lagranges multiplier method to find optimal solution To maximize/ minimize f(x,y,z)…

Q: Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that…

A: Given equation 2x2+72y2=72which can be writtenx236+y21=1

Q: rectangle of maximum perimeter is to be inscibed in the ellipse x^2/22^2 + y^2/12^2 = 1. The…

A: Using lagrange multipliers.

Q: Obtain the differentialequation of the family of ellipses w/center at (0, 0) having major and minor…

A: We will form the Differential equation.

Q: The plane x + y + 2z = 6 intersects the paraboloid z = x2 + y² in an ellipse. Find the points on…

A: To find the farthest and nearest point from the origin to the ellipse.

Q: Find an equation of the ellipse with foci at (-5,9) and (-5,-10) and whose major axis has length 22.…

Q: 7. If the latus rectum of an ellipse with axis along x-axis and centre at origin is 10, distance…

Q: A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/20^2 +y^2/11^2=1. The…

A: Explained below

Q: x, y From a variable point of an ellipse - + 2 = Inormal is drawn to the ellipse. %3D a' b? Find the…

Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

A: NOTE: Refresh your page if you can't see any equations. . The diameter of the dish is 18 feet and…

Q: Describe the graph of the equation. r = 5 costi - 19 sin rj+k O An ellipse in the planex = 1, center…

A: The graph of the given equation is ; r = 5 cost i - 19 sint j + k We have to choose the correct…

Q: Determine the eccentricity of a hyperbola with a horizontal transverse axis of length 24 units and…

Q: 4x^2 + y^2 = 4 that are the farthest away from point (1,0)

Q: Find the orthogonal trajectories of family of hyperbola with center at the original and the length…

A: The solution are next step

Q: 11. Show that the tangent to the hyperbola x- y = 1 at the pomt P(coshu, sinhu), cuts the x-axis at…

A: We will be using the definition of tangent line to solve the problem

Q: Find the area of the resulting surface if an arc of a parabola y=x2 from (1,1) to (2,4) is rotated…

A: The given curve is: y=x2 from (1, 1) to (2, 4)

Q: The plane x + y + 2z = 20 intersects the paraboloid z = x² + y² in an ellipse. Find the points on…

Q: Sana wants to recycle some elliptic cardboard into rectangular name plates. The minor and major axes…

A: Given problem is : Sana wants to recycle some elliptic cardboard into rectangular name plates. The…

Concept explainers

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.

Question

At a point A(1, 1) on ellipse, equation of tangent is y = x. If one of the foci of ellipse is (0, -2) and the co-ordinates of center of ellipse are (a, b) then the value of a + b is (Given length of major axis of ellipse is 4√10 units)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Ellipses$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

Similar questions

Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.
By definition, an ellipse is the locus of points whose sum of distances from two fixed points F1 and F2 called foci is constant. In the grid provided, find points whose sum of distances from points F13, 0 and F2-3, 0 is 10. That is, locate some points for which PF1+PF2=10; point P5, 0 is one such point. Then sketch the ellipse.
Two friends visit a whispering gallery (in the shape of a semi-ellipsoid) wherethey stand 100 m apart to be at the foci. If one of them is 6 m from thenearest wall, how high is the gallery at its center?
A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/22^2 + y^2/10^2 = 1. The rectangle's sides are parallel to the axes of the ellipse. Find the larger dimension of this rectangle. Round off to two decimal places.
A flashlight is shaped like a paraboloid and the light source is placed at the focus so that the light bounces off parallel to the axis of symmetry, this is done to maximize illumina- tion. a particular flashlight has its light source located 1 cm from the base and is 6 cm deep. what is the width of the flashlight's opening?
A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/20^2 + y^2/12^2 = 1. The rectangle's sides are parallel to the axes of the ellipse. Find the larger dimension of this rectangle. Answer should be in two decimal places.
Sana wants to recycle some elliptic cardboard into rectangular name plates. The minor and major axes of each ellipse are of lengths 10 cm and 20 cm, respectively. What should be the dimensions of each name plate so that the usage of cardboard materials is maximized? The equatiion is (x2/25)+(y2/100)=1.
A suspension bridge with weight uniformily distributed along its length has twin towers that extend 80 meters above the road surface and are 1200 meters apart. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cables at a point 300 meters from the center. (Assume the road is level)
A long suspension bridge 180 meters from end,has towers 60 meters tall,where suspension cables are attached at the top of each tower.The cable from a parabolic curve and the lowest point of the cable is 15 meters from the surface of the bridge. Which set of information is true to the scenario described?
The region bounded by the ellipse 16?^2 + 9?^2 = 144 is revolved about the x-axis. Find thevolume of the solid generated. (WITH GRAPH)
determine a and b as to make the cylinder y^2=4ax orthogonal to the ellipsoid at point (1,2,1)
A reflecting telescope contains a mirror shaped like a paraboloid of revolution.If the mirror is 4 inches across at its opening and is 3 inches deep,where will the collected light be concentrated?