TS EAMCET · Maths · Hyperbola
The product of the perpendicular distances from any point on the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) to its asymptotes is
- A \(\frac{a^2 b^2}{a^2-b^2}\)
- B \(\frac{a^2 b^2}{a^2+b^2}\)
- C \(\frac{a^2+b^2}{a^2 b^2}\)
- D \(\frac{a^2-b^2}{a^2 b^2}\)
Answer & Solution
Correct Answer
(B) \(\frac{a^2 b^2}{a^2+b^2}\)
Step-by-step Solution
Detailed explanation
Let \((a \sec \theta, b \tan \theta)\) be any point on the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) The equation of the asymptotes of the given hyperbola are \(\left(\frac{x}{a}+\frac{y}{b}\right)=0 \text { and }\left(\frac{x}{a}-\frac{y}{b}\right)=0\) Now, \(P_1=\)…
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