identify the conic of the equation 4x² + 9y² − 16x + 18y = 11, specifying the center and radius if it is a circle; the foci and the sum of the focal rays if it is an ellipse; and the focuses and the difference of the focal rays if it's hyperbole.

Q: Find the standard form of the equation of the ellipse satisfying the following conditions. vertices…

A: Given:Vertices of major axis: (-2,12) and (-2,4)Length of minor axis is 4

Q: Complete the square to determine whether the graph of the equation is an ellipse, a parabola, a…

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Q: Complete the square to determine whether the graph of the equation is an ellipse, a parabola, a…

A: 3x2+4y2-12x-24y+48=0 3x2-12x+4y2-24y+48=0 3(x2-4x)+4(y2-6y)=-48…

Q: The center of the ellipse with the given equation 4(x – 5)2 + 3(y – 4)2 = 48 is

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Q: Find the standard form of the equation of the ellipse and give the location of its foci.

A: Consider the given figure: It is an ellipse with center origin.

Q: Find the focus, equation of the directrices, lengths of major axis, minor axis and focal diameters,…

A: The given equation is 16x2+4y2=1. The general equation of the ellipse is x2a2+y2b2=1 and b>a.…

Q: Find the standard form of the equation of the ellipse and give the location of its foci.

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Q: Find an equation of the hyperbola whose foci are the vertices of the ellipse 4x2+9y2=36 and whose…

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Q: the equation of the ellipse is given by 4x^(2)+9y^(2)+24x-18y+9=0.find its center,semi axis,and the…

A: Given equation, 4x2+9y2+24x-18y+9=0                         ...(1)

Q: Write the equation of the ellipse in standard rectangular form that has foci at ( 2 , − 2 ) a n d (…

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Q: Convert the equation 36x2 + 9y2 - 216x = 0 to standard form by completing the square on x and y.…

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Q: 5. Find the vertices and foci of the ellipse given by the equation. 4x +9y² - 32x–36y+64=0

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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: Find an equation of the ellipse whose foci are the vertices of the hyperbola x2-4y2=16 and whose…

A: We know that,              Hyperbola vertices given x2-4y2=16:  4, 0, -4, 0Hyperbola foci given…

Q: Convert the equation 4x2 + 9y2 - 32x + 36y + 64 = 0 to standard form by completing the square on x…

A:

Q: Find the focus, equation of the directrices, lengths of major axis, minor axis and focal diameters,…

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Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic section y2 -…

A: y2-4x2+16x=24 On simplification, we get…

Q: Find an equation of the ellipse having a major axis of length 10 and foci at (2, -2) and (2, –8).…

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Q: Decide if the equation defines an ellipse, a hyperbola, a parabola,or no conic section at all. 4x 2−…

A: An equation has to have x2 or y2 to be an equation of any conic sections. If, in an equation neither…

Q: Write an equation of an ellipse with the center (2, -4 ), and with a vertical major axis of length…

A: General equation of ellipse having vertical major axis is given by÷   x-h2b2+y-k2a2=1 Where,…

Q: Express the equation of an ellipse 16x² +9y² – 64x-54y+1=0 in standard form. Hence, find the centre,…

A: The standard form of equation of ellipse is x-x02a2+y-y02b2=1 and eccentricity of ellipse is…

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: Decide if the equation defines an ellipse, a hyperbola, a parabola,or no conic section at all. 4y 2…

A: Given equation is 4y2+9x2=12. To determine whether the equation defined an ellipse, a hyperbola,…

Q: Find the standard form of the equation of the ellipse and give the location of its foci. Ay 6- 4- 12…

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Q: What is the standard form equation of the ellipse that has vertices (±6, 0) and co-vertices (0, ±5)?…

A: We have to find the equation of the ellipse with given vertices and co-vertices.

Q: Find the center, vertices, foci, and eccentricity of the ellipse. 6x^2+2y^2+30x-18y+54=0

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Q: Find an equation of the ellipse having a major axis of length 10 and foci at (5,-1) and (-1, -1).…

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Q: I was given a study packet (not graded) and I'm not sure I'm going about getting the equation into…

A: Given:

Q: Convert the equation 49x2 + 16y2 + 98x - 64y - 671 = 0 to standard form by completing the square on…

A: Given equation is 49x2+6y2+98x-64y-671=0 To convert the given equation into standard from by…

Q: Graph the conic section with the given equation x2 = -8y. For ellipses, find the foci. For…

A: Given, x2=-8y

Q: The eccentricity of the ellipse x2/4+y2/16=1 is:

A: Given equation of ellipse: x24+y216=1

Q: Graph the conic section with the given equation 4x2 - y2 + 8x + 2y + 7 = 0.For ellipse, find the…

A: Given the equation of conics, 4x2-y2+8x+2y+7=0

Q: Convert the equation 16x2 + 25y2 - 300y + 500 = 0 to standard form by completing the square on x and…

A: Convert the equation 16x2 + 25y2 - 300y + 500 = 0 to standard form by completing the square on x and…

Q: 1. Find the center, the vertices, focijland eccentricity of the ellipse given by the equation a) 3x2…

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Q: Express the equation of an ellipse 16x+9y-64x-54y+13D0 in standard form. Hence, find the centre,…

A: General equation of eclipse is x-h2b2+y-k2a2=1 centre of eclipse = ( h , k ) Vertices = (h,k+a) ,…

Q: Find an equation of the ellipse that has center (0, -4), a minor axis of length 4, and a vertex at…

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Q: Find the standard form for the equation of the hyperbola with foci (0,0) and (8,0) if the conjugate…

A: Standard form of equation of hyperbola.

Q: Graph the conic section with the given equation 9x2 - 4y2 = 36.For ellipse, find the foci. For…

A: Given: The equation of conic section as 9x2-4y2=36, To sketch: The graph of given conic section, To…

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

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Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate,of the conic sections y2 -…

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Q: Convert the equation 9x2 + 25y2 - 36x + 50y - 164 = 0 to standard form by completing the square on x…

A: Consider the given equation, 9x2+25y2-36x+50y-164=0 complete the square on x and y as follows,…

Q: Find an equation of the ellipse that has center (2, -4), a minor axis of length 2, and a vertex at…

A: Trace the equation

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

A: Given: eccentricity=1/2 passing through (1,3)

Q: Convert the equation to standard form by completing the square on x and y. Then graph the ellipse…

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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: Find the center, foci, vertices, and eccentricity of the ellipse…

A: 9x2+4y2+36x-24y-36=0⇒9x2+36x+4y2-24y=36⇒9x2+4x+4y2-6y=36⇒9x2+4x+4+4y2-6y+9=36+36+36⇒9x+22+4y-32=108⇒…

Q: Select the conic section represented by the equation. x 2 +y 2 + 6x - 4y - 12 = 0. circle point…

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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.