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C is the center of the hyperbola (x^2)/(...

`C` is the center of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` The tangent at any point `P` on this hyperbola meet the straight lines `b x-a y=0` and `b x+a y=0` at points `Qa n dR` , respectively. Then prove that `C QdotC R=a^2+b^2dot`

A

`a^(2)+b^(2)`

B

`a^(2)-b^(2)`

C

`(1)/(a^(2))+(1)/(b^(2))`

D

`(1)/(a^(2))-(1)/(b^(2))`

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The correct Answer is:
A
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ML KHANNA-THE HYPERBOLA -PROBLEM SET (2) (MCQ)
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  2. C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangen...

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  3. Find the equation of the tagent to the hyperbola x^(2)-4y^(2)=36 which...

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  4. The point of intersection of two tangents to the hyperbola (x^(2))/(a^...

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  5. The line y=x+2 touches the hyperbola 5x^2-9y^2=45 at the point

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  6. 2x+sqrt(6)y=2 touches the hyperbola x^(2)-2y^(2)=4, then the point of ...

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  7. The product of the lengths of the perpendiculars drawn from foci on an...

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  8. A common tangent to 9x^(2) - 16y^(2) = 144 and x^(2) + y^(2) = 9 is

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  9. If the chord through the points (a sec theta, b tan theta) and (a sec ...

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  10. Find the equations to the common tangents to the two hyperbolas (x^2)/...

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  11. The value of m for which y=mx+6 is a tangent to the hyperbola (x^(2))/...

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  12. Tangents which are parrallel to the line 2x+y+8=0 are drawn to hyperb...

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  13. The equation of the tangent to the hyperbola 4y^(2)=x^(2)-1 at the poi...

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  14. If ax+by+c=0 is a normal to hyperbola xy=1, then (A) alt0, blt0 (B) al...

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  15. If the tangent and normal to a rectangular hyperbola cut off intercept...

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  16. If (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(agtb) and x^(2)-y^(2)=c^(2) cut a...

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  17. Let P(asectheta,btantheta) and Q(asecphi,btanphi), where theta+phi=(pi...

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  18. If the normal at (ct(1),c//t(1)) on the curve xy=c^(2) meets the curve...

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  19. P Q and R S are two perpendicular chords of the rectangular hyperbola ...

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  20. If the normal at P to the rectangular hyperbola x^2-y^2=4 meets the ax...

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