Find an equation for the set of points P(x, y) in a plane the sum of whose distances from two fixed points F1(0, 2) and F1(0, – 2) is a constant 6. Hint: What type of graph has the given condition?

Q: What will be the axis of symmetry, the line about which a figure or curve is upon itself, between…

A: Given :   y=4x-2

Q: Find the shortest distance, d, from the point (11, 0, –6) to the plane x + y + z = 6. = p

A:

Q: The curve r(t) (2t, 3 - 1,0) is a line that passes through the origin.

A: We are given a curve r(t) = < 2t, 3-t ,0 > which is a line. To find : If the line passes…

Q: Prove that for any point (a, b) ≠ (0, 0) on the parabola y = x2 , the normal line intersects the…

A: The given equation of parabola is y=x2  For the point (a,b)≠ (0, 0), the slope of normal is and at…

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: H

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A:

Q: 4. Find the equation of the locus of the points P(x, y) whose distances from the point (3,2) are…

A:

Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

Q: Find the point (a, b) on the graph of y = ex where the value ab is theleast.

A:

Q: Find the coordinates of the intersection points A and B, between the closed curve (x + 1)² + 4(y-1)²…

A: In this question, we can find the intersection points of the given curve. Using the equation of…

Q: Plot the points (with whole number coordinates) that satisfy the equation below and fit onto the…

A:

Q: Find a plane containing the point (6, -4,-3) and the line (t) = +t 270

A:

Q: The point (a,b) and (c,d) are points on the graph of y= x3+5 whose tangent lines are perpendicular…

A: y=x3+5slope at a,b =2x2=2a2     ...(1)slope at c,d =2x2=2c2     ...(2)slope of given line = -13…

Q: The graph shows the normal lines from the point (2,0) to the graph of the parabola x = y?. How many…

A:

Q: A5: What is the minimum (perpendicular) distance from the point p = (-1,–2) to the line L := 4x = 14…

A:

Q: Find the length of the curve r=θ^2 from θ=0 to θ=6

A: Given: -

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: Find all hyperbolic lines that passes through i +1 and parallel to the y-axis.

A: Find all hyperbolic lines that passes through i+1 and parallelto the y-axis.

Q: For what minimum integer value of a, will the line ax+(a+1) y =18 www (a> 0) have two intersection…

A: If the line cuts the circle at two points then given line is secant line of the circle .The…

Q: Find the midpoint of points A(8, –7) and B(3, –1) graphically. Plot the line segment AB by clicking…

A: The graph is shown below:

Q: Exercises 1–6, sketch the given curves together in the appropriate coordinate plane and label each…

A:

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: Parametrization is a way to change the parameters of a expression in such a way that domain of the…

Q: Find a relationship between x and y such that (x, y) is equidistant the same distance from the two…

A: Given points are: 4,-1 and -2,3 The distance between the points 4,-1 and x,y is: d1=x-42+y+12 The…

Q: Describe with a sketch the sets of points 1x, y, z2 satisfying the following equations. y - z = 0

A: First sketch the graph of the function y-z=0 as shown below.

Q: 3) Sketch the graph For the Following Functiones. a) 2: 3-2x-6y b) Plane 23+Z =H H

A: We shall give graph of the 3d diagrams in next steps. We shall sketch for first 3 subparts only.

Q: The graphs of r +y² + 6x – 24y + 72 = 0 and x² - y' + 6x + 16y - 46 0 intersect at four points.…

A: We have to find distance from given point to intersecting points of given equation. And then add all…

Q: An equation for the level surface passing through the point (2,0, - 1) is z =

A:

Q: Find the shortest distance, d, from the point (6, 0, -4) to the plane x + y + z = 4.

A: The shortest distance of a point from a plane is said to be along the line perpendicular to the…

Q: Prove that the curves y2 = 4x and y2-6x+1 = 0 touch each other at the point (1,2)

A:

Q: Sketch the graph for c=0 and then explain how the graphs (level curves or surfaces) change for the…

A: Given f(x, y, z)=x2-y+z2 To find the graph we need to find level surface of equation, equate the…

Q: Prove that the curves y2 = 4x and x2+ y2-6x+1 = 0 touch each other at the point (1,2)

A:

Q: 8) Determine if the line given by r(t) = intersects the xz-plane. If so, determine at what point.

A: we have to find the point of intersection.

Q: Find the number  a such that the line x = a  bisects thearea under the curve  y = 1 / x 2  , 1<…

A: Our Aim is to find a number such that line x=a bisects the area under the curve y=1x2, 1≤x≤4.

Q: Find the relation between x and y such that the point (x,y) is equidistant from the points (7,1) and…

A:

Q: Use slopes to verify that the graphs of the equations Ax + By = C and Bx - Ay = D are perpendicular.…

A:

Q: =r = 2 and r = 4cos.

A: Intersection points in polar coordinates given in the form as (r, theta).

Q: 1. Which of the following points in the standard (x, y) coordinate plane is farthest from the…

A: Find the distance of each given point from origin Using distance formula.

Q: Verify that the two families of curves are orthogonal, where C and K are real numbers. Use a…

A: xy=C,  x2-y2=K Consider, xy=C Differentiating with respect to x, we get…

Q: The equation of the curve in the tx-plane which passes through the point (2,3), and has, at every…

A: In this question, slope of curve and point is given and we have to find out equation of cuve.

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Equidistant points mean that the distance of two points represented by P1 and P2 is equal to the…

Q: 3 z 2 1 -2 -1 2

A:

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: y=0, z=0

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given parametric curve is, x=2ty=8t3-1≤t≤1 From the parameter of x, x=2tt=x2

Q: Consider the parabola f (x) = x² – 4x and the line g(x) = –2x – 1. Determine the %3D point(s) of…

A: Given parabola,y=x2-4x                     (1)Given line y=-2x-1                     (2)Put value of…

Q: A curve on the ry-plane passes through the point (0, a) for some number a, and has the property that…

A:

Q: A curve C has equation y =x2lnx- 2x +5, x > 0. %3D For which values of x, the curve C is convex?

A: The equation of the given curve is  y=13x2 ln x-2x+5 , x>0 For the curve to be convex its second…

Q: 3. Find the length of the curve y = x - In a, 1< x < 4.

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: 5. The coordinates of the vertex of the curve y = 1- 2x - 4x² are: A. G ) B. (- 5 ) €(- ) D.(- -) 1…

A: Hi, for question 6 repost

Q: Sketch the graph of the following quadratic surfaces a) 4x² +9y² + z² = 36 b) x² - y²z² = 1 c) x²…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

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.