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If the transformed equation of a curve i...

If the transformed equation of a curve is `X^(2) - 2XY tan 2 alpha - Y^(2) = a^(2)` when the axes are rotated through an angle `alpha` , then the original equation of the curve is

A

`x^(2) + y^(2) = a^(2) cos 2 alpha`

B

`x^(2) - y^(2) = a^(2) cos 2 alpha`

C

`x^(2) + a^(2) = y^(2) cos 2 alpha `

D

`x^(2) - a^(2) = y^(2) cos 2 alpha`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-CHANGE OF AXES-Exercise - 1
  1. Assertion (A) : If the area of triangle formed by (0,0), (-1,2),(1,2) ...

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  2. If the axes are rotated through an angle of 45^(0) and the point p has...

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  3. If the axes are rotated through an angle 45^(0) in the anti-clockwise...

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  4. The angle of rotation of axes in order to eliminate xy term of the equ...

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  5. The angle of rotation of axes to remove xy term of the equation xy = ...

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  6. The transformed equation of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 when th...

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  7. The transformed equation of x^(2) + y^(2) = r^(2) when the axes rotate...

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  8. The transformed equation of 3x^(2) + 3y^(2) + 2xy =2 when the coordina...

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  9. When angle of rotation of axes is Tan^(-1) 2 the transformed equation...

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  10. When axes rotated through an angle alpha the transformed equation of x...

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  11. If the transformed equation of a curve is X^(2) - 2XY tan 2 alpha - Y^...

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  12. Find the angle of rotation of the axes so that the equation sqrt(3) x ...

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  13. Find the angle of roation of the axes so that the equation 2x + 3y =7...

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  14. If the point (sqrt(2), - sqrt(2)) was transformed as (0, -2) by rotat...

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  15. Statement - I : The point to which the origin has to be shifted to el...

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  16. The origin is translated to (1,2) . The point (7,5) in the old system ...

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  17. The point P(1,3) undergoes the following transformations successively ...

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  18. If the origin of a coordinate system is shifted to (-sqrt(2), sqrt(2))...

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  19. If the coordinate axes are rotated through an angle (pi)/(6) about the...

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  20. If the axes are rotated anticlockwise through an angle 90^(@) then the...

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