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AP EAMCET · Maths · Hyperbola

The product of the perpendicular distances drawn from any point on the hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) to its asymptotes is

  1. A \(\frac{13}{36}\)
  2. B \(\frac{13}{5}\)
  3. C \(\frac{36}{13}\)
  4. D \(\frac{36}{5}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{36}{13}\)

Step-by-step Solution

Detailed explanation

Asymptotes of \(\frac{x^2}{9}-\frac{y^2}{4}=1\) are \(\frac{x}{3} \pm \frac{y}{2} = 0 \Rightarrow 2x \pm 3y = 0\). Product of perpendicular distances \(P = \frac{|(2x-3y)(2x+3y)|}{\sqrt{2^2+(-3)^2}\sqrt{2^2+3^2}}\). \(P = \frac{|4x^2-9y^2|}{13}\). From the hyperbola equation,…