Which graph represents the ellipse given by x^2/20+y^2/28=1?

Q: Find an equation for parabola with vertex  (−1,3) and directrix x=−4.

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Q: Find the coordinates of the vertices of the ellipse with foci at (-6,-3) and (10,-3) and has minor…

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Q: What is the standard form equation of the ellipse that has vertices (-6, –13) and (-6,7) and foci…

A: Given that, vertices of ellips are, (-6, -13)   and   (-6, 7) foci of the ellips are, (-6, -4)   and…

Q: What is the equation of a parabola in vertex form with vertex (-5, -9) and directrix y = -13?

A: The parabola has vertex -5,-9 and directrix y=-13

Q: What is the equation that represents an ellipse with foci at (3, 2) and (-9, 2) that passes through…

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Q: Write the equation in standard form of the conic with the given characteristics: Hyperbola: vertices…

A: Write the equation in standard form of the conic with the given characteristics: Hyperbola: vertices…

Q: Find the equation of ellipse in stand form with center at the origin Endpoints of minor axis (+10,…

A: Here we have to find the equation of the ellipse in the standard form with center at the origin.…

Q: Find lengths of minor and major axis for ellipse that has equation 16x2 + 4y2 = 16

A: Given, 16x2 + 4y2 = 16

Q: A certain bridge arch is in the shape of half an ellipse 148 feet wide and 32.1 feet high. At what…

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Q: 2- Write the equation of hyperbola that pass through point (12, 9) and have F1 (0, 0) and F2 (0, 4)V

A: Consider the given information. y−k2a2−x−h2b2=1 Since we have the given foci at F1(0,0) and F2(0,4).…

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 of the ellipse having a major axis of length 10 and foci at (-3, 3) and (- 3, – 3).

A: This is a problem of locus and analytical geometry.

Q: Find the standard form of the equation of ellipse satisfying the given conditions as  Major axis…

A: It is given that an ellipse whose major axis is horizontal with length 8, length of minor axis is…

Q: Find the point on the ellipse 4x2ty3=4 that are farthest away from the point (1,0) 4x27y2-4

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Q: Which point on the graph of the parabola y 4x has the minimum distance between the graph and the…

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Q: What is the equation of the given ellipse? YA

A: Vertex ( -3 , 2 ) covertex ( -1 , -1.5 )   Center= ( h , k )= ( -3 , - 1.5 )   Major axis b = 2 - (…

Q: Find the standard form of the equation the ellipse whose major axis is vertical with length 10, with…

A: standard form of ellipse is(x-h)2b2+(y-k)2a2=1where(h,k)≡(-2,3)b=4 and a=10therefore equation of…

Q: What is the equation of the hyperbola with vertices at (-3,0) and (3,0) and whose conjugate axis has…

A: Hyperbola A hyperbola is a locus of points in such a way that the distance to each focus is a…

Q: Find the equation of a parabola whose vertex is located at (2, −3) and whose focus is located at…

A: Given: vertex: 2,-3focus: 0,-3 To Find: Equation of a parabola. Concept: Horizontal…

Q: The line segment perpendicular to the axis of symmetry, passing through the focus and with endpoints…

A: Given:The line segment perpendicular to the axis of symmetry, passing through the focus and with…

Q: What is the equation of parabola in standard form whose focus is at (-4,0) and the directrix is at…

A: Note that, the equation of the parabola with the directrix x+a=0 and the focus (a,0) is y2=4ax.

Q: The line passing through the vertex that divides the parabola into two symmetric parts is . The two…

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Q: Discuss the graph of the ellipse with foci at (2, 3) and (2, −1) and an endpoint of the minor axis…

A: The mid-point of the foci is equal to the center of the ellipse, so O(h,k)=2+22,3+(-1)2=2,1 If the…

Q: Which graph represents the ellipse given by x^2/4+y^2/1=1?

A: Given equation of ellipse is x24+y21=1. We know that the standard equation of ellipse is given as:…

Q: what is the equation of a parabola with a vertex at (4, 8) and a directrix at y=5

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Q: Which graph corresponds to an ellipse with foci located at ((2+2√5), 6) and ((2−2√5), 6) and the…

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Q: Write the standard form equation of the ellipse. Major axis vertical with length 16. Minor axis…

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Q: What is the standard form equation of an ellipse with the center (-1, 6), a horizontal major axis…

A: Center (h,k) = (-1,6) a = 22 b = 8

Q: What is the standard form equation of the ellipse that has vertices (−6,−13) and (−6,7) and foci…

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Q: Find an equation for the hyperbola that satisfies the Vertices: (±1, 0), asymptotes: y = ±3x

A: Given,        Vertices: (±1, 0)    asymptotes: y=±3x

Q: Find an equation of the ellipse having a major axis of length 12 and foci at (0, 5) and (0, 1). =D ?

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Q: Find the equation for the ellipse with center (0,0), vertices (-5,0) and (5,0) and foci: (-4,0) and…

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Q: Find the standard form of the equation of the hyperbola.

A: It is given in the figure that, the vertices of the hyperbola are 0 , ±5 and the length of the…

Q: A large racetrack can be modeled by the ellipse x² + y2 1, where x and y are 4 measured in…

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

Q: Write the equation of hyperbola that pass through point (12, 9) and have F1 (0, 0) and F2 (0, 4)

A: Since you have posted multiple question but according to guidelines, we will solve first question…

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

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Q: Find the coordinates of the vertices of the ellipse with foci at (-6,-3) and (10,-3) and has minor…

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Q: Find an equation of the hyperbola having foci at (-2, 6) and (-2, 12) and vertices at (-2, 8) (-2,…

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Q: What point on the parabola y = 3- x² is closest to the point (3,3)? The point on the parabola y = 3…

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Q: Find the dimensions of the rectangle with maximum perimeter that can be inscribed with sides…

A: Assume the length of rectangle be 2x and width of the rectangle be 2y. Therefore, the perimeter is…

Q: Find the standard form of the equation of an ellipse with the given characteristics. Major axis…

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Q: 17. Ellipse: center (-2, 1), vertex (-2,5), passes through (0, 1)

A: Equations of curve is

Q: 2- Write the equation of hyperbola that pass through point (12, 9) and have F, (0, 0) and F2 (0, 4).

A: Since, the foci of the given hyperbola are F′(0,0​) and F(0,4​) which lie on the X-axis and…

Q: What point on the parabola y = 5-x is closest to the point (5,5)? The point on the parabola y = 5- x…

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Q: One successful method to treat kidney stones is by emerging the patient in an elliptical tank and…

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Q: Find an equation of the hyperbola having foci at (-6, 4) and (8, 4) and vertices at (-1,4) (3, 4).…

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Q: What is the equation of a horizontal ellipse with a center at point (-2,4), a major axis that is 8…

A: Given : Center (-2,4), Length of major axis = 8 units Length of minor axis = 4 units   To find :…

Q: How does the shape of the ellipse change as varies?

A: Explanation: The ellipse stretches vertically when the value of b increases.

Q: Suppose the axis of a parabola is parallel to the yy-axis and passing through the points (0,3),…

A: Given that, the axis of a parabola is parallel to the y-axis. Let the Vertex of the parabola (h, k)…

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.