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Let any double ordinate P N P ' of the h...

Let any double ordinate `P N P '` of the hyperbola `(x^2)/(25)-(y^2)/(16)=1` be produced on both sides to meet the asymptotes in `Qa n dQ '` . Then `P QdotP^(prime)Q` is equal to 25 (b) 16 (c) 41 (d) none of these

A

25

B

16

C

41

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`NP=(4)/(5)sqrt(x_(1)^(2)-25)`
Point Q is on
`y=(4)/(5)x`
`NQ=(4)/(5)x_(1)`
`PQ=NQ-NP`
`=(4)/(5)(x_(1)-sqrt(x_(1)^(2)-25))`
`P'Q=(4)/(5)(x_(1)+sqrt(x_(1)^(2)-25))`
`PQ*P'Q=16`
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CENGAGE-HYPERBOLA-Exercise (Single)
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  3. Let any double ordinate P N P ' of the hyperbola (x^2)/(25)-(y^2)/(16)...

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  4. For hyperbola whose center is at (1, 2) and the asymptotes are paralle...

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  5. The asymptotes of the hyperbola (x^(2))/(a(1)^(2))-(y^(2))/(b(1)^(2))=...

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  6. If S=0 is the equation of the hyperbola x^2+4x y+3y^2-4x+2y+1=0 , then...

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  7. If two distinct tangents can be drawn from the Point (alpha,2) on diff...

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  8. A hyperbola passes through (2,3) and has asymptotes 3x-4y+5=0 and 12 x...

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  9. From any point to the hyperbola ^2/a^2-y^2/b^2=1, tangents are drawn ...

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  10. The combined equation of the asymptotes of the hyperbola 2x^2 + 5xy + ...

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  11. The asymptotes of the hyperbola x y=h x+k y are x-k=0 and y-h=0 x+h=0...

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  12. The center of a rectangular hyperbola lies on the line y=2xdot If one ...

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  13. The equation of a rectangular hyperbola whose asymptotes are x=3 and y...

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  14. If tangents O Q and O R are dawn to variable circles having radius r a...

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  15. Four points are such that the line joining any two points is perpendic...

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  16. If S1a n dS2 are the foci of the hyperbola whose length of the transve...

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  17. Suppose the circle having equation x^2+y^2=3 intersects the rectangula...

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  18. The equation of the chord joining two points (x(1),y(1)) and (x(2),y(2...

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  19. The locus of the foot of the perpendicular from the center of the h...

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  20. The curve xy = c(c > 0) and the circle x^2 +y^2=1 touch at two points,...

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