Question

The value of m for which $y = mx + 6$ is a tangent to the

hyperbola $\frac{x^{2}}{100} - \frac{y^{2}}{49} = 1$, is

• A. $y = \pm \frac{b}{a}x$
• B. $\sqrt{\frac{20}{17}}$
• C. $x^{2} - y^{2} = a^{2}$
• D. $\sqrt{\frac{20}{3}}$

Answer 1

Answer: (A)

$y = \pm \frac{b}{a}x$

Answer 2

For condition of tangency, $c^{2} = a^{2}m^{2} - b^{2}$ . Here $c = \lambda$, $a = 10,b = 7$

Then, $(6)^{2} = (10)^{2}.m^{2} - (7)^{2}$

$36 = 100m^{2} - 49$ ⇒ $100m^{2} = 85$ ⇒ $m^{2} = \frac{17}{20}$ ⇒ $m = \sqrt{\frac{17}{20}}$