Find the equation of the ellipsoid passing through the points (+5, 0, 0), (0, +6, 0) and (0, 0, +7) = 1

Q: Find an equation of the ellipse that has center (0, 5), a major axis of length 4, and endpoint of…

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Q: Find an equation of the sphere that passes through the origin and whose center is (3, 1, 4).

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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: Find an equation for the conic whose graph is shown. y (4, 3) 2. 2.

A: Since given shape is  ellipse . So will use standard equation of it .

Q: I need help in this question of the conic section. Find the equation of the ellipse whose center at…

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Q: Find the equation of the hyperboloid of one sheet passing through the points (±2,0,0), (0, ±7,0) and…

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Q: Find the center, vertices and foci of the ellipse x² +4 y² -8 x-8 y= 44 Select one: O Center = (…

A: Equation of the given ellipse is x2+4y2-8x-8y=44. Rewrite the above equation in standard form…

Q: Parameterize an ellipse which begins at (-3, 3) at t=0 and then passes through (-6, 1), (-3, -1),…

A: First we have to find equation of ellipse in rectangular coordinate.

Q: Find an equation of the sphere that passes through the point (6, –2, 3) and has center (-1, 2, 1).

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Q: Find the largest and smallest distances from the origin to the conic whose equation is 5x2 − 6xy +…

A: To find the largest and smallest distances from the origin to the conic whose equation is 5x2 − 6xy…

Q: Find the equation of the conic section indicated. Parabola with vertex (4, −1), directrix x = 15

A: Vertex is 4, -1 and directrix is x=15. Now vertex is, h, k=4, -1⇒h=4  &  k=-1 & Directrix…

Q: Find an equation for the ellipse with Center at: (0, 0) Foci at: (+5, 0) Vertices at: (±6, 0)

A: 6. The ellipse have center at 0,0 , foci ±5,0 and vertices ±6,0  Note: Multiple questions are given,…

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

A: Let (x,y) is the farthest point on the ellipse from (1,0) Distance between (x,y) and (1,0) is:…

Q: Find an equation of the line in parametric form that passes through the vertex of the paraboloid…

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Q: -6 4 -2 19 6 4 2 2 6

A: The standard form of the equation of a hyperbola with center (h,k)(h,k) and transverse axis parallel…

Q: How can you determine the type of conic section represented by an equation in general form?

A: Types of conic section and general equation

Q: Find the equation of the hyperboloid of one sheet passing through the points (±8,0,0), (0, ±3,0) and…

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Q: I. Directions: ldentify the center of each ellipse. 1. (x+4) 2 16 + (y-3) 24 = 1 Center: 2. (x-4)…

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Q: Find an equation of the sphere that passes through the point (1, 8, 5) and has center (3, 1, −3).

A: We have to find equation of sphere.

Q: Find an equation of the sphere that passes through the origin and whose center is (1, 2, 3).

A: I have appended the formula used in the solution part.

Q: Find the coordinates of the foci of the ellipse with vertices at (11,3) and (-15,3) and has minor…

A: To find the coordinates of the foci of the ellipse with vertices at 11, 3 and -15, 3 and has minor…

Q: What is the equation of the ellipse with the center at (0.0) that passes through the points (2,0),…

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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: Q1. Find the equation of sphere with center (1, 2,-1) passing through the point (-1, 2, 1).

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Q: Find an equation of the ellipsoid which passes through (1,1, 2), (0,0, 3), (1,2, 1) and has the…

A: If a, b, and c are the principal semi axes, and the center of the ellipsoid is at the point of…

Q: find the equation of the conic section indicated Ellipse with vertices (±8, 0), foci (±√3, 0)

A: Coordinates of vertices - ±a, 0 = ±8, 0a = 8Coordinates of foci - ±c, 0 = ±3, 0c = 3Let's find b -…

Q: Find the orthogonal trajectories of the family of ellipses with centers at (0, 0) and two vertices…

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Q: Find an equation for the conic that satisfies the given conditions. parabola, vertical axis, passing…

A: A parabola with vertices passing through 0,5,1,4, and -2,-5. Find the equation for the conic that…

Q: Find an equation for the conic section with the given properties. The hyperbola with foci F1(3, -5)…

A: We have to find the equation of the conic section.

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 equation of the hyperboloid of one sheet passing through the points (+2, 0,0), (0, ±6, 0)…

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Q: Find the equation in xy coordinates for the conic section that satisfies the 4 following conditions:…

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

Q: Find the point (x, y) on the ellipse, 4(x - 1)^2+ y^2 = 1, that is farthest to the origin (0, 0).

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Q: find the equation of an ellipse with a center at (0,0) and focus at (1,0) and vertex at (5,0)

A: Since the center , vertex and focus all are on the x-axis, so the standard form of the ellipse will…

Q: Find an equation of the sphere that passes through the point (8, 1, -5) and has center (5, 6, 3).

A: The objective of the question is determine the question of sphere .

Q: Find an equation for the conic whose graph is shown. y F (6, 0)

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Q: Find the equation of the ellipsoid passing through the points (+8, 0, 0), (0,±7,0) and (0,0, ±3) = 1

A: The standard equation of an ellipsoid is x2a2+ y2b2 + z2c2=1where a, b , c are the length of its…

Q: What is the general equation of the conic section passing through the points  A(0,1), B(2,3),…

A: Given points A(0,1), B(2,3), C(5,4), D(1, −2), E(4, −1)   General equation:  ax2 + bxy + cy2 +…

Q: What are the foci of the ellipse given by (z-3)2 (y-1)2 - = 1? 25 O (-4, 1) and (4, 1) O (3, 5) and…

A: Topic : foci of an ellipse

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

A: Given 3x2+y2=3

Q: 6. Find an equation of the sphere that passes through the origin and whose center is (3, 1, 3).

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

A:

Q: Find the equation of the hyperboloid of one sheet passing through the points (+8, 0, 0), (0, +6, 0)…

A:

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

A: To find the points on the ellipse 5x2+y2=5, that are farthest away from the point 1, 0.

Q: Find the equation of the ellipsoid passing through the points (±3,0,0), (0, ±4, 0) and (0,0,±7) = 1

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Q: Find an equation for the conic that satisfies the given conditions. hyperbola, vertices (-1, -3),…

A: If the general equation of the hyperbola is: -(x-h)2a2+(y-k)2b2=1 Then, vertices are at (h, b+k),…

Q: Determine the center of the conic of equation: 16x² + 128r + 49y² + 588y = -1236. A) (4,6) В) (-4,…

A: Brief explanation of the answer is below.

Q: Find an equation of the ellipse that has center (0, 3),

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Q: Find an equation for the conic that satisfies the given conditions. hyperbola, vertices (-1, -3),…

A: To find the equation of hyperbola that satisfy the following conditions- vertices(-1, -3) , (-1, 5)…

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.