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Show that product of lengths of the perp...

Show that product of lengths of the perpendicular from any point on the hyperbola `x^(2)/(16)-y^(2)/(9)=1` to its asymptotes is `(144)/(25)`.

A

144/9

B

144/25

C

144/16

D

25/144

Text Solution

Verified by Experts

The correct Answer is:
B
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AAKASH SERIES-HYPERBOLA-Practice Exercise
  1. The radius of the auxiliary circle of the hyperbola x^(2)//25-y^(2)//9...

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  2. The equation of the normal to the hyperbola x^(2)-4y^2=5 at (3,-1) is

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  3. Tangents to the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 makes angles theta...

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  4. Tangents are drawn to 3x^(2)-2y^(2)=6 from a point P. If the product o...

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  5. The chords of contact al P.w.r.t. x^(2)-y^(2)=a^2 and x^(2)+y^(2)=a^(2...

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  6. The equation to the common tangent to the hyperbolas (x^(2))/(25)-y^(2...

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  7. The point of intersection of two tangents to hyperbola x^(2)/a^(2)-y^(...

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  8. The locus of the midpoints of chords of the hyperbola 3x^(2)-2y^(2)+4x...

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  9. The mid point of the chord x+2y+3=0 of the hyperbola x^(2)-y^(2)=4 is

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  10. The equation of the tangent to the hyperola x^(2)/9-y^(2)/4=1 at the p...

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  11. Equation of normal to x^(2)-4y^(2)=5 at theta=45^(@) is

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  12. The equation of asymptotes of the hyperbola 4x^(2)-9y^(2)=36 is

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  13. The equation to the pair of asymptotes of the hyperola 2x^(2)-y^(2)=1 ...

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  14. Show that product of lengths of the perpendicular from any point on th...

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  15. The equation of one asymptote of the hyperbola 14x^(2)+38y+20y^(2)+x-7...

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  16. The equation of the hyperbola is xy-4x+3y=0 and its asymptotes are xy-...

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  17. The equation of the hyperbola whose asymptotes are 3x+4y-2=0, 2x+y+1=0...

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  18. No part of the hyperbola x^(2)/(a^(2))-y^(2)/b^(2)=1. Lies between whi...

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  19. Assertion (A): The pair of asymtotes of x^(2)/(10)-y^(2)/4=1 and the p...

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  20. A hyperbola whose transverse axis is along the major of the conic, (x^...

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