iCoachMath.com: Examples on Rotation of Conics - Analytical Geometry in Two and Three Dimensions

Curriculum: Alaska Math Grade Level Expectations Click to change Curriculum

Topic: Analytical Geometry in Two and Three Dimensions Click to change Topic

Lesson: M.A.4: Rotation of Conics Click to change Lesson

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e Choose the coordinates of the point P (9, 0) in original system, when the original system is rotated through an angle π4.
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e Choose the angle to which the axes are to be rotated to remove the x' y' - term in the transformed equation of 5x² + 4xy + 5y² - 48 = 0. e

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e Find the type of conic represented by the equation 5x² + 53xy + 125y² = 1. e

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e Choose the coordinates of a point (- 4, - 4) when the axes are turned through an angle 90°. e

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e The transformed equation of a conic after the axis are rotated through some angle is given by x² + 143xy + 3y² + (6 + 33)x + (63 - 3)y + 14 = 0. The conic is ________. e

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e Choose the new coordinates of the point (- 5, 4) when the axes are rotated through an angle 30°.
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e Choose the coordinates of the point P (0, 4) in the original system, when the original system is rotated through an angle π3. e

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e Choose the angle to which the axes are to be rotated to remove the x' y' - term in the transformed equation of 4x² + 8xy - 8y⁸ + 3x + y + 16 = 0. e

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e Find the angle of rotation needed to remove the x' y' - term in the transformed equation of the equation 3x² + 53xy - 2y² = 1.
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e Evaluate : ∑k=1n (k² + k)
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e Evaluate : ∑k=1n(k³ + k) e

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e Choose the original coordinates of a point P in terms of new coordinates, when the axes are rotated through an angle θ without changing the origin, where (x, y) and (x′, y′) be the original and new coordinates.
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e Choose the new coordinates of a point P in terms of original coordinates, when the axes are rotated through an angle θ without changing the origin, where (x, y) and (x′, y′) be the original and new coordinates.
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e Choose the new coordinates of the point (- 7, 6) when the axes are rotated through an angle 30°.
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e Choose the angle to which the axes are to be rotated so that the x' y' term in the translated equation of Ax² + Bxy + Cy² + Dx + Ey + F = 0 will not be present.
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e Choose the coordinates of a point (- 3, - 3) when the axes are turned through an angle 90°. e

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e Choose the coordinates of the point P (8, 0) in original system, when the original system is rotated through an angle π4.
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e Choose the coordinates of the point P (0, 10) in the original system, when the original system is rotated through an angle π3. e

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e Choose the conic, which is represented by the equation x² - xy + y² = 2 when it is rotated through a suitable angle.
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e The transformed equation of a conic after the axis are rotated through some angle is given by x² + 353xy + 5y² + (7 + 53)x + (73 - 5)y + 35 = 0. The conic is ________. e

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e Choose the angle to which the axes are to be rotated to remove the x' y' - term in the transformed equation of 9x² + 3xy + 9y² - 14 = 0. e

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e Choose the angle to which the axes are to be rotated to remove the x' y'-term in the transformed equation of x² + 3xy - 2 = 0.
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e Choose the angle to which the axes are to be rotated to remove the x' y' - term in the transformed equation of 9x² + 18xy - 13y² + 3x + y + 47 = 0. e

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e Choose the angle to which the axes are to be rotated to remove the x' y' - term in the transformed equation of 48x² + 83xy + 24y² = 0. e

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e Find the transformed equation of x² + 23xy - y² = 2a², when the axes are rotated through an angle π6.
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e Find the transformed equation of 17x² - 16xy + 17y² = 225, when the axes are turned through an angle π4.
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e What type of conic does the equation 5x² + 46xy + 4y² - 2x + 8y - 45 = 0 represent?
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e Choose the transformed equation of 4x² - 4xy + 7y² - 24 = 0, when the axes are turned through an angle π4. e

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e Find the transformed equation of x² - y² = a², when the axes are turned through an angle π4. e

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ccc Find the transformed equation in the standard form, which is free from the x′y′ - term of the conic 13x2+63xy+ 7y2 = 16. ccc

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ccc Find the type of conic represented by the equation 6x² + 23xy + 72y² = 1. ccc

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ccc Find the transformed equation of 4xy - 3x² = a² when the axes are turned through an angle tan-1(2). ccc

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ccc Find the transformed equation in the standard form for the conic x² + 23xy - y² = 2a².
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ccc Find the angle of rotation needed to remove the x' y' - term in the transformed equation of the equation 5x² + 93xy - 4y² = 1.
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ccc What type of conic does the equation 3x² + 19xy + 5y² - 3x + 4y - 18 = 0 represent?
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ccc The transformed equation of Ax2+Bxy+Cy2 = 0, when the axes are rotated through an angle θ is A′x′2+B′x′y′+C′y′2 = 0 then find the value of B′² - 4A′C′. ccc

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ccc Evaluate : ∑k=1n (k² + k)
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ccc Evaluate : ∑k=1n(k³ + k) ccc

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ccc Find the transformed equation of 5x2+3xy+y2 = 5. Identify the type of conic that the transformed equation would represent.
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ccc Choose the angle to which the axes are to be rotated to remove the x' y' - term in the transformed equation of 12x² + 23xy + 6y² = 0. ccc

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ccc Evaluate : ∑m=1n ∑k=1m k ccc

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ccc Evaluate : ∑m=1n ∑k=1m k ccc

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