IGDTUW 2025 — Mathematics PYQ

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Question

IGDTUW 2025 — Mathematics PYQ

IGDTUW | Mathematics | 2025

The equation of the tangent to the hyperbola $\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1$ parallel to the line $3x - 2y + 5 = 0$ is:

Choose the correct answer:

Explanation

Solution

Hyperbola se values:

$a^2 = 9$ aur $b^2 = 4$ .
Slope ( $m$ ) nikaalein:

Line $3x - 2y + 5 = 0$ ko $y = mx + c$ ke roop mein likhne par:

$2y = 3x + 5 \implies y = \frac{3}{2}x + \frac{5}{2}$

Isliye, $m = \frac{3}{2}$ .
Tangent ki equation ka formula:

Hyperbola ke liye tangent ki equation hoti hai: $y = mx \pm \sqrt{a^2m^2 - b^2}$

$y = \frac{3}{2}x \pm \sqrt{9 \left( \frac{3}{2} \right)^2 - 4}$

$y = \frac{3}{2}x \pm \sqrt{9 \left( \frac{9}{4} \right) - 4}$

$y = \frac{3}{2}x \pm \sqrt{\frac{81}{4} - 4} = \frac{3}{2}x \pm \sqrt{\frac{81 - 16}{4}}$

$y = \frac{3}{2}x \pm \frac{\sqrt{65}}{2}$

Sahi jawab option (a) hai.