Question

The angle between the tangents from (–2, –1) to the hyperbola 2x² – 3y² = 6 is-

• A. tan­–1(2)
• B. $\frac{\pi}{3}$
• C. tan–1$\left( \frac{1}{2} \right)$
• D. $\frac{\pi}{6}$

Answer 1

Answer: (C)

tan–1$\left( \frac{1}{2} \right)$

Answer 2

$\frac{x^{2}}{3}–\frac{y^{2}}{2}$ = 1; y + 1 = m (x + 2) or y = mx + (2m – 1) touches the hyperbola

if “c2 = a2m2 – b2” if (2m – 1)2 = 3m2 – 2

(i.e.) if m2 – 4m + 3 = 0 giving m = 1 and 3.

tan q = $\left| \frac{3–1}{1 + 3 \times 1} \right|$ = $\frac{1}{2}$

Ž q = tan–1$\left( \frac{1}{2} \right)$