Find the general equation of the ellipse that shares a vertex and a focus with the parabola defined by y2 – 4x – 2y + 9 = 0 and whose other vertex is at (12, 1). Draw the conics.

Q: Identify the conic section that equation 16x^2-96x+288=9y^2 represents and find either: a) it’s foci…

A: We use completing square method to convert it into standard form

Q: identify the conic of the equation 4x² + 9y² − 16x + 18y = 11, specifying the center and radius if…

A: The standard equation of a conic section is defined by the equation, Ax2+Bxy+Cy2+Dx+Ey+F=0 .

Q: 20) Write the equation of the ellipse 4x +9y +24x 162y + 729 = 0 in standard form and then graph the…

A: Given the equation of the ellipse, 4x2+9y2+24x-162y+729=0

Q: The equation of the ellipse that has its center at the origin with focus at (0, 4) and vertex at (0,…

A: The ellipse has its center at the origin with focus at 0,4 and vertex at 0,7

Q: O Does the origin lie inside or outside the ellipse with equation (x – 4) 2 + 4(y - 3) 2 = 4?

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Q: Find the standard form of the ellipse given below in general form. x2 – 2x + 4y2 + 24y + 33 = 0

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Q: 2. Find the equations of all horizontal parabolas whose focus is the center of the ellipse 9a? +17y²…

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Q: Find an equation for the ellipse that has its center at the origin and satisfies the given…

A: The center of the ellipse is 0,0. The vertices of the ellipse are  0,7 and 0,-7. The focus of the…

Q: The equation of the ellipse that has a center at (10, 1), a focus at (7, 1), and a vertex at (15, 1)…

A: Given: Center (10,1) Vertex (15,1) focus (7,1)

Q: 3.Determine the equation of an ellipse that satisfies the following properties: - the center point…

A:

Q: Find an equation for the ellipse that has its center at the origin and satisfies the given…

A: Vertices V (0,±5), minor axis of length 3

Q: Write an equation for the ellipse centered at the origin with a major axis 14 units long with…

A:

Q: Find an equation for the ellipse that shares a vertex and a focus with the parabola y2 + 4x = 36 and…

A:

Q: Give the equation in standard form of the ellipse centered at the origin with a focus at (0, 2), and…

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Q: Find an equation for the ellipse that has its center at the origin and satisfies the given…

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

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

A: The distance between the endpoints of the minor axis is equal to 2b, so…

Q: Find the standard form of the equation of the conic section satisfying the given conditions,…

A: Given focus is (-2,6) and the directrix is x=8.

Q: Convert the equation 25x2 + 4y2 - 150x + 32y + 189 = 0 to standard form by completing the square on…

A: Given: The equation of ellipse as 25x2+4y2-150x+32y+189=0 To find: the standard equation of ellipse,…

Q: Find the equation of the hyperbola with vertices at (- 2, 0) and (2, 0) and a focus at (4, 0)

A: Given the hyperbola with vertices at (- 2, 0) and (2, 0) and a focus at (4, 0)

Q: Find an equation for the ellipse. Center at (0, 0); focus at (3, 0); vertex at (4, 0)

A: SOLUTION-

Q: Find an equation for the hyperbola with center C(0,0), foci F(0,±9), and vertices V(0,±7).

A: Plotting the center, foci, vertices on the graph. We can say that the vertical axis is the…

Q: 19. The center of the ellipse 4x2 + y2 -16x - 6y – 43 = 0 is at: %3D

A:

Q: Convert the general equation of the ellipse 3x^2+4y^2-6x-24y+3=0 into standard form and give the…

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Q: Find the standard equation of the ellipse whose major and minor axes are the transverse and…

A: We need to find standard equation of ellipse.

Q: Find the standard form of the equation of the ellipse with the given characteristics. y 10 2 N 4…

A:

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

A: Standard form of ellipse

Q: Find the point on the ellipse x2 + 6y² + 3xy = 40 with the largest x-coordinate (Figure ). -8 FIGURE…

A: Given: x2+6y2+3xy=40

Q: Determine the equation of the hyperbola with center (−1, −6), a focus at (−1, −16), and a co-vertex…

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Q: Find an equation for the ellipse. Center at (0, 0); focus at (-2, 0); vertex at (7, 0)

A: According to question given that Center (0,0), focus (-2,0), vertex (7,0)We have to find the…

Q: 1. Give the coordinates of the foci, vertices and covertices of the ellipse with equation 169 x2 y²…

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Q: Consider the following. У 2 1- -3 -1 3 4 -1 -2 Find an equation of the ellipse. Find its foci. (х,…

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Q: Consider the parabola P with equation x^2 = 20 (y - k) and whose directrix has equation y = −7. The…

A: This question is related to conic section , we will use the give conditions to find the equation of…

Q: 4. Find an equation for the ellipse with Center at: (0, 0) Focus at: (2, 0) Vertex at: (5, 0)

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Q: Find the equation in standard form of the ellipse whose foci are F1(-8, and F2(8, 0), such that for…

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Q: Determine what type of conic section corresponds to the given equation. (3x + y)² – 2y = x Ellipse.…

A: We have to check the given equation.

Q: Find the equation of Hyperbola using only the following information: Center at (0, 0) Vertices at…

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Q: What will be the equation of the ellipse with a center at the origin and passes through the points…

A: Given query is to find the equation of ellipse.

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

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Q: Find the equation of the ellipse whose foci are at (2,1 ) and ( 6,1),and the length of its major…

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Q: The equation of the ellipse that has a center at (4, 1), a focus at (0, 1), and a vertex at (– 1,…

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Q: Find the center of the ellipse given by x² – 2x + 2y? - 12y +3 0. Enter as an ordered pair without…

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Q: The equation of the ellipse that has a center at (6, 1), a focus at (10, 1), and a vertex at (1, 1),…

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Q: Find the standard equation of the parabola opening to the left whose axis contains the major axis of…

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Q: Identify the general equation, as well as the coordinates of the foci of the following ellipse that…

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Q: 9x2 - 18x + 4y +8y = 23 defines an ellipse with center ( 1 -1 ). The major axis has length and the…

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Q: The equation of the ellipse that has a center at (7, 3), a focus at (4, 3), and a vertex at (12, 3),…

A:

Q: Find the standard equation of the ellipse whose foci are F,(-3, 0) and F2(3, 0), such that for any…

A: Given:   Foci : (-3,0) (3,0)    Distance from foci : 10

Q: For the equation 9x + 4y - 54x-8y-59 = 0, classify the conic section, put the equation in standard…

A: Explanation: Given that,  9x2+4y2-54x-8y-59=0   Here we use the completing the square method in term…

Q: Find the general equation of the ellipse that shares a vertex and a focus with the parabola defined…

A: For the equation of the parabola , the vertex is and the focus is . For the equation of the ellipse…

Q: The ellipse 15x^2+2x+y^2=1 has its center at the point (b,c) where b = c=

A: To find the center at the point b, c of the ellipse,15x2+2x+y2=1b=?c=?

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.