Island 1 Island 2 12 mi - Not drawn to scale

Q: The solid whose base is the triangle with vertices (0, 0), (2, 0), and (0, 2), and whose cross…

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Q: Determine the greatest and least distance from the origin to a point on the ellipsoid 9x2+4y2+z2=36

A: Here is the solution of the given problem. Application of Lagranges Multiplayer.

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

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Q: Find the coordinates of the foci of an ellipse with center at (-1,2), one co-vertex at (2,2), and…

A: Given problem:- Find the coordinates of the foci of an ellipse with center at (-1,2), one co-vertex…

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: Find the points on the ellipse 4x + y² = 4 that are farthest away from the point (1, 0). (х, у) %3D…

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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: A rectangle is to be inscribed inside a semi-ellipse + = 1, -2 <IS2 and 0 y S 3. Give a rough sketch…

A: Solution is here

Q: What is the equation of an ellipse with its center at (-2, 1), a major axis 16 units long, and…

A: Write equation of parabola

Q: The base of an object is an ellipse with axis lengths of 10 cm and 8 cm. Since the intersection of…

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Q: A rod of given length (a+b) unit moves so that its ends are always on coordinates. Prove that the…

A: The two ends of the rod is always on coordinate axes. Let's take one end P of the rod is always on X…

Q: Show that the horizontal traces of the ellipsoid are ellipses of the same eccentricity (apart from…

A: To show Horizontal traces of the ellipsoid x2a2+y2b2+z2c2=1are ellipses of  same eccentricity

Q: Find the standard form of the question of the ellipse with given characteristics and center at the…

A: This is a problem related to conics section. Based on the general formula and concept we will…

Q: 2. The arch of a bridge is in the shape of a semi ellipse having a horizontal span of 40 meters and…

A: To find the height at the required value then you should have the equation of the ellipse.

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

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

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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…

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Q: Find the equation of the ellipse that has center C (0, 4), foci F1 (0,0) and F, (0, 8), and major…

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Q: A searchlight is shaped like a paraboloid of revolution.If the light source is located 2 feet from…

A: draw the parabola used to form the searchlight on a rectangular coordinate system so that the vertex…

Q: The plane 9x + 12y+ 40z = 275 intersects the cone z = coordinates of the highest and lowest points…

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Q: 15.A satellite dish has a shape called a paraboloid, so that Ito crous-sections through its center…

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Q: the sum of the distances from (x,y) to (-1,0) and from (x,y) to (1,0) is 4. show x and y is related…

A: Distance from (x,y) to (-1,0) is:  Distance from (x,y) to (1,0) is:

Q: find the standard form of the equahon of the ellipse with the given characteristics verhical major…

A: let equation of ellipse isx2a2+y2b2=1

Q: What is the equation in standard form of an ellipse whose center is at C(-3, 1), a vertex at V(-5,…

A: NOTE: Refresh your page if you can't see any equations. . the standard form of the ellipse is given…

Q: Find the points on the ellipse 3x + y = 3 that are farthest away from the point (1, 0). smaller…

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Q: Find the standard form of the équation of the ellipse satisfying the given conditions. Endpoints of…

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Q: Find the coordinates of the foci of an ellipse with center at (-1,2), one co-vertex at (2,2), and…

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Q: A one-way tunnel has the shape of a semi ellipse that is 12ft high at the center and 28H across. a.…

A: If the semi-ellipse is 12ft high at the center and 28 ft across then  The length of the major axis,…

Q: The length of the major axis of the cllipse with center (-4, 1), minor axis parallel to the y-axis…

A: Equation of ellipse with center (-4,1) is given by

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: O An ellipse in the plane x axis, minor axis of length 14 parallel to the y-axis. = 1, center at (1,…

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Q: 3. What are the lengths of the major and minor axes of this ellipse = 1? Major Axis: 6 units, Minor…

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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: 2. What are the foci of this ellipse? 5 -5 O (-1, –4V5) and (–1, 4v5) O (-1, –2/5) and (-1,2/5) O…

A: By carefully examining the figure we will find that the major axis should pass through the line x =…

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

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Q: Find the standard form of equation of the ellipse that satisfies the given conditions. a. Center at…

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Q: At a point A(1, 1) on ellipse, equation of tangent is y = x. If one of the foci of ellipse is (0,…

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Q: Find the intersection points of the pair of ellipses. (100x? + 25y2 = 100 y2 x2 + 1 = (х, у)…

A: Given : Ellipses equation            100x2 + 25y2 = 100   .....(1)             x2 + y2/9 = 1…

Q: DId entify, and find the goneraLequabion of the ellipse that ghares avertex and focus with the para…

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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: What are the intersections of the conic section formed by the points A(0,1),B(2,3),C(5,4),D(1,…

A: Below are graph and input view.

Q: A mirror for a reflecting telescope has the shape of a (finite) paraboloid of diameter 8 inches and…

A: It is given that, A mirror for a reflecting telescope has the shape of a (finite) paraboloid of…

Q: Find the dimensions of the rectangle of largest perimeter that can be inscribed in the ellipse x2/a2…

A: Let 2x,2y be the length and width of the ellipse that is inscribed in ellipse  Then , perimeter of…

Q: What is the standard form of the ellipse with center at (0,0),vertex at (0,9) and co vertex (4,0)

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

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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…

Q: Deandre, an engineering intern was asked by his fellow students to heip them determine the standard…

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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.