Q. The value of $m$, for which the line $y = mx + 2\$ becomes a tangent to the conic $4x^{2} - 9y^{2} = 36$ are
A) $\pm \frac{2}{3}$
B) $\pm \frac{2\sqrt{2}}{3}$
C) $\pm \frac{8}{9}$
D) $\pm \frac{4\sqrt{2}}{3}$
Explanation
(b)
Given, $y = mx + 2$
and $\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1\$
Condition of tangency, $c = \pm \sqrt{a^{2}m^{2} - b^{2}}$
$2 = \pm \sqrt{9m^{2} - 4}\ \Rightarrow \ m = \pm \frac{2\sqrt{2}}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.