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Find the condition that the equation ax^...

Find the condition that the equation `ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c = 0` to take the form `aX^(2) + 2hXY + bY^(2) = 0` when the axes are translated.

A

`abc + 2fgh - af^(2) - bg^(2) - ch^(2) = 0`

B

`2byh - ab^(2) - by^(2) - ch^(2) = 0`

C

`abc - ab^(2) - by^(2) - ch^(2) = 0`

D

`abc + 2gh = 0`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-CHANGE OF AXES-Exercise - 1
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  2. (6,6) is a point on the circle x^(2) + y^(2) - 4x - 6y - 12 = 0 by tra...

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  3. Find the condition that the equation ax^(2) + 2hxy + by^(2) + 2gx + 2f...

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  4. Assertion (A) : If the area of triangle formed by (0,0), (-1,2),(1,2) ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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