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B Choose the coordinates of P (7, 8) in the translated coordinate system, when the origin is shifted to the point P (- 7, 13) without changing the direction of axes.
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B Identitfy the type of conic represented by the equation 7x2 - 2xy + 8y2 - 20x + 70y - 17 = 0.
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| B Identify the type of conic represented by the equation 3x2 - 2y2 - 2y - 48 = 0. B |
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| B Choose the equation in standard form for the given conic. [Given a = 9, b = 6.] B |
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B Choose the co-ordinates of P(15, - 7) in the rotated system, if the axes are rotated through an angle π3.
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B Find the discriminant of the equation 5xy - 4 = 0.
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| B Find the approximate angle of rotation needed to eliminate the cross product (or) x' y' term in the transformed equation of 9x2 + 2xy + 3y2 - 44 = 0. B |
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B Identify the curve the equation (x - 4)2 = 2(y - 8)2 repesents.
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B Choose the conic represented by the equation 4y2 + 24y - 4x2 + 16x = -4.
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B Choose the angle to which the axes need to be rotated to remove the x′ y' terms in the transformed equation of 12x2 + 23xy + 6y2 = 0.
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| B Choose the point to which the axes may be translated so as to remove the first degree terms in the transformed equation of 4x2 + 5xy - 6y2 + 4x + 5y + 10 = 0. B |
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B Choose the coordinates of P (5, 6) in the translated coordinate system, when the origin is shifted to the point P (- 5, 11) without changing the direction of axes.
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B Find the discriminant of the equation 9xy - 8 = 0.
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B Identify the curve the equation (x - 3)2 = 4(y - 6)2 repesents.
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B Choose the original coordinates of a point P in a plane when the origin O is shifted to the point O'(h, k) without changing the direction of the axes, where (x, y) represents the original coordinates and (x′, y′) represents the changed one.
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B Choose the translated coordinates of a point P in a plane when the origin O is shifted to the point O'(h, k) without changing the direction of the axes, where (x, y) and (x′, y′) are the coordinates of the point P referred to original and new axes.
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B Choose the coordinates of a point P in a plane when the axes are rotated through an angle α, where (x, y) and (x′, y′) are coordinates of original and rotated axes.
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B Choose the angle to which the axes need to be rotated to remove the cross-product term (x'y' - term) in the translated equation of the original equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.
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B Choose the condition when the second degree equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 represents a parabola.
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B Choose the condition when the second degree equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 represents an ellipse.
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B Choose the condition when the second degree equation Ax2 + Bxy + Cy2 + Dx + Ey + f = 0 represents a hyperbola.
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B Identitfy the type of conic represented by the equation 4x2 - 3xy + 5y2 - 30x + 40y - 31 = 0.
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| B Identify the type of conic represented by the equation 9x2 - 9y2 - 3y - 31 = 0. B |
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| B Choose the equation in standard form for the given conic. [Given a = 7, b = 5.] B |
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B Choose the co-ordinates of P(17, - 8) in the rotated system, if the axes are rotated through an angle π3.
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B Choose the conic represented by the equation 4y2 + 32y - 4x2 + 24x = -12.
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B Write an equation in standard form for the conic shown.
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B Which of the following is true about the conic Ax2 + Cy2 + Dx + Ey + F = 0?
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B Identify the transformed equation of x² + 23xy - y² = 2a², when the axes are rotated through an angle π6.
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| B Find the approximate angle of rotation needed to eliminate the cross product (or) x' y' term in the transformed equation of 9x2 + 5xy + 3y2 - 11 = 0. B |
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B Which of the following equations represents the standard form of the conic 16x2 - y2 - 32x - 6y - 57 = 0? Translate the axes so that the origin is at the center.
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B Find the discriminant of the tranformed equation of Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 when the axes are translated to (h, k).
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B Choose the angle to which the axes need to be rotated to remove the x′ y' terms in the transformed equation of 11x2 + 23xy + 5y2 = 0.
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| B Choose the point to which the axes may be translated so as to remove the first degree terms in the transformed equation of Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. B |
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| B Choose the point to which the axes may be translated so as to remove the first degree terms in the transformed equation of 3x2 + 4xy - 5y2 + 3x + 7y + 22 = 0. B |
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B Choose the point to which the axes may be translated so as to remove the first degree terms in the transformed equation of xy + 4x - 5y - 16 = 0.
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B Choose the point to which the axes may be translated so as to remove the first degree terms in the transformed equation of xy + 2x - 3y - 36 = 0.
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