ExamBro
ExamBro
AP EAMCET · Maths · Hyperbola

If \(3 x+2 \sqrt{2} y+k=0\) is a normal to the hyperbola \(4 x^2-9 y^2-36=0\) making positive intercepts on both the axes, then \(\mathrm{k}=\)

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

Answer & Solution

Correct Answer

(D) \(-13 \sqrt{2}\)

Step-by-step Solution

Detailed explanation

Hyperbola: \( \frac{x^2}{9} - \frac{y^2}{4} = 1 \) \(a^2=9, b^2=4\) Normal equation at \( (x_1, y_1) \): \( \frac{a^2x}{x_1} + \frac{b^2y}{y_1} = a^2+b^2 \) \( \frac{9x}{x_1} + \frac{4y}{y_1} = 13 \) Given normal: \( 3x + 2\sqrt{2}y = -k \) Comparing coefficients:…