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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

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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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