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TS EAMCET · Maths · Hyperbola

\((p, q)\) is the point of intersection of a latus rectum and an asymptote of the hyperbola \(9 x^2-16 y^2=144\). If \(p\gt0\) and \(q\gt0\) then \(q=\)

  1. A \(\frac{9}{4}\)
  2. B \(\frac{7}{4}\)
  3. C \(\frac{15}{4}\)
  4. D \(\frac{13}{4}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{15}{4}\)

Step-by-step Solution

Detailed explanation

\(9 x^2-16 y^2=144\) \(\Rightarrow \frac{x^2}{16}-\frac{y^2}{9}=1 \Rightarrow a^2=16, b^2=9, e=\frac{5}{4}\) Equation of latus rectum, \(x= \pm a e\) \(\Rightarrow x= \pm 5 \qquad ...\mathrm{(i)}\) Equation of hyperbola asymptote is…