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The locus of the point of intersection o...

The locus of the point of intersection of the tangents at the ends of normal chord of the hyperbola `x^(2)-y^(2)=a^2` is

A

`y^(4)-x^(4)=4a^(2)x^(2)y^(2)`

B

`y^(4)-x^(2)=4a^(2)x^(2)y^(2)`

C

`a^(2)(y^(2)-x^(2))=4x^(2)y^(2)`

D

`y^(2)+x^(2)=4a^(2)x^(2)y^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-HYPERBOLA-Exercise -II
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  2. If the intercepts made by tangent, normal to a rectangular hyperbola x...

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  3. If the normal at theta on the hyperbola x^(2)//a^(2)-y^(2)//b^(2)=1 me...

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  4. If the l x+ my=1 is a normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/...

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  5. The locus of the point of intersection of the tangents at the ends of ...

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  6. The locus of middle points of normal chords of the rectangular hyperbo...

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  7. The maximum number of normals to hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 f...

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  8. The product of lengths of the perpendiculars from the point of the hyp...

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  9. The product of lengths of the perpendiculars from the point of the hyp...

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  10. The angle between the asymptotes of the hyperbola x^(2) -3y^(2) =3 i...

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  11. The asymptotes of the hyperbola 6x^(2) +13xy +6y^(2) -7x -8y-26 =0 ar...

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  12. The assymptotes of the hyperbola are parallel to 3x+2y=0, 2x+3y=0 whos...

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  13. If 2x^(2)+5xy+2y^(2)-11x-7y+K=0 is the pair of asymptotes of the hyper...

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  14. The line x+y+1=0 is an asymptote of x^(2)-y^(2)+x-y-2=0. The other asy...

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  15. The equation of a line passing through the centre of a rectangular hyp...

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  16. The area of the triangle formed by any tangent to the hyperbola x^(2)...

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  17. Statement-I : The combined equatioin of the pair of asymptotes of the ...

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  18. If x= 9 is a chord of contact of the hyperbola x^(2) -y^(2) =9, then ...

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  19. If the circle x^(2)+y^(2)=r^(2) intersects the hyperbola xy=c^(2) in f...

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  20. The area (in square units) of the equilateral triangle formed by the t...

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