Calculate the equation of the system of conic sections with basic points A(1,2); B(2,0); C(-1,1); D(0,3). Ans. k(-4 x² + y² + 2xz-7yz+12 z²)+1(-3x² + 4xy + 4y²-3xz-18 yz+18 z²) = 0

Q: Q14: Use the properties of diagonalization of matrices to identify the given conic section:…

A: Given an equation for a conic section: Q: .One can write this equation in matrix form as .Let…

Q: Find the equation of the conic in the rotated system that eliminates the cross-product term and find…

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Q: section

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Q: Graph the conic section 2x² - 12x - y² + 6y+26=0 by completing the square.

A: The given equation is .The aim is to sketch the graph of the conic section.

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

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Q: Find a new representation of 2x² + 8xy - 1 = 0 by describing it in a system with axes rotated by…

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Q: 3. Find the vertex for the parabola 4x + 2y² + 8 = 0. (a) (0, -2) (b) (-2,0) (c) (2, 2) (d) (-2,1)

A: The equation of the parabola is  4x+2y2+8=0

Q: The parabola shown in the figure has an equation of the form y = ax² + bx + c -5 y 5 (2, 4), -5 -10…

A: The parabola shown in the figure has an equation of the form .The parabola passes through the points…

Q: Find the point on the hyperbola x²-9y² 9 where the line 5x + 12y = 9 touches it.

A: Solving                  5x+12y=9  or            y=9-5x12   and   x2-9y2=9  We have…

Q: Find the center of 8x 2 + 6y 2 - 32x + 24y + 8 = 0. (2, 2) (-2, 2) (2, -2)

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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: Which of the following properties satisfy the parabola with equation x² + 6x + 8y = 7 O v(3,2);…

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Q: (b) Find for what value of the equation 12x²+36xy + y² + 6x + 6y + 3 = 0 represents a pair of…

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Q: A. Transform each equation to center-radius form and determine its center and radius. 1. x² + y²…

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Q: The cylinder x² + y² = 25 intersects the plane x + z = 5 in an ellipse. Find the point on such an…

A: Given:The cylinder is: .The plane is .The cylinder intersects the plane in an ellipse.

Q: 4) Transform the parabolic equations (9)40xxt120xy けy-20x +0こo x+9 (6) e2x Uxx +2e**Jxy+ e®Uyy=O to…

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Q: Find the equation of the hyperbola with vertices at (-4,2) and (0,2) and foci at (-5,2) and (1,2).…

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Q: The vertex of the parabola given by the equation x2 = 20 y is O (0,0) O (4,5) O (0,5) O (4,0)

A: Vertex of the parabola

Q: Write the equation in standard form, identify the conic and the location of its center or vertex:…

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

Q: Q5: Find the coordinates of vertices of the hyperbola x² – 4y2 – 4x – 8y – 4 = 0 - - (-1,4),(-1,0)…

A: We have to find vertices of hyperbola.

Q: Find the values of integers,, and c that will make the hyperbola -9x² + 4y² + ax +by+c= 0 pass…

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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: Find the center of the ellipse 16x² +9y² - 64x - 54y + 1 = 0 (a)_(-2, 3) (b) (-2, -3) (c)_(2, -3)…

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Q: 11x2-7y2-66x-28y-6=0 standard form of hyperbola

A: Given    standard form of Hyperbola

Q: The center of the hyperbola 25x² – y + 150x – 6y+191=0 is %3D A (-3,-3) B (3,-3) (3,3) D (-3,3)

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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…