What is the standard form of the conic defined by x + 2y² – 8y = 0?

Q: Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic.xy − 8x − 4y…

A: We have to determine the type of conic of the given equation by performing the rotation of axes to…

Q: 1) x² + y² + 30x – 16y+285 = 0

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

Q: Performa a rotation of axes to eliminate the xy-term of the conic 9x2 +4xy+9y2-20 = 0. Identify the…

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Q: Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic.x2 + 2xy + y2…

A: Comparing the given equation with Ax2+Bxy+Cy2+Dx+Ey+F=0, we get, A=1, B=2, C=1, D=2, E=-2 and F=0.…

Q: 3. Transform into standard form and identify the conic sections: a) 92²-4y²-36x-24y-35-0. b) x²-3xy…

A: 9x2-4y2-36x-24y-35=0

Q: 5. Sketch the graph and find the coordinates of the foci for the conic 4(x+2)² =36-9(y−1)²

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Q: 6. Find the equations of the asymptotes for the conic 25x²-150x-16y²-64y-239=0

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Q: 2) Foci: (2, –5 + V61), (2, –5 – V61) 20 5 Asymptotes: y ==x- 6 3 y-- 5 10 ソ=ーーX 6 3

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Q: Identify the conic with th e given equa­tion and give its equation in standard form…

A: Given:  A conic of equation 3x2-4xy+3y2-282x+222y+84=0. To Find: The given conic also write it ina…

Q: y? – 4y + 4x 16 = 0 is the equation of a conic. Write the standard form of that conic. |

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Q: (b) The equation 7x2 - 3xy + 5y² + 4x - 16y- 121 = 0 represents a non-degenerate conic. (i)…

A: We have to find the type of conic of given equation

Q: Select a possible equation for a parabola with a vertex of (-1,3). Oy = (z + 1) (x – 3) | Oy = (z -…

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Q: Q.8: ] find the parametrization of the upper half of the conic section 4x² +9y²-24x = 0; with x= -2

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Q: 20) Find the coordinàtes of the foci of the conic x² –10x –16y² – 64y – 55= 0

A: We write the given conic in standard form Then we compare it with the standard equation of a…

Q: 1. Determine what type of conic the equation 9x² - 4y² + 54x + 16y + 29 = 0, represents, find all…

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Q: Q15: A quadratic form is given by; 5x² - 2xy + 5y² = 24. Identify the conic section and illustrate…

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Q: 5x 2 − 3xy + 4y 2 − 8x + 10y − 64 = 0 represents a non-degenerate conic Determine the type of…

A: Sign of discriminant i.e. B2-4AC determine the nature of non-degenerate conic.

Q: 5. Write the equation of the following conic 12 11 10 4 3 2 -1 3 5 fo 11 12 -1 -2

A: The given conic is the ellipse with  1. Center (8,5)  2. Vertex1: (8,12) 3. Vertex2: (8,-2) 4.…

Q: 16. Which equation represents the given parabola?

A: We want to find the equation of given parabola.

Q: x² – 9y2 : -9y2 = 13 x² + y² = 53 %3D

A: Given,

Q: O Reduce the equation x + 2ry +y +4 V2x - 4V2y = 0 to the standard form and hence %3D identify the…

A: The given equation is x2+2xy+y2+42x-42y=0

Q: Identify and sketch the conic defined by x2 - 2xy+ y² – x – y=0.

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Q: Study and draw the conic section Q(x, y) = 13x² + 13y² — 10xy = 36. -

A: Conic sections (including degenerate ones) are the sets of points whose coordinates satisfy a…