Q. If $4x - 3y + k = 0\$touches the ellipse $5x^{2} + 9y = 45$, then $k$ is equal to
A) $\pm 3\sqrt{21}$
B) $3\sqrt{21}$
C) $- 3\sqrt{21}$
D) $2\sqrt{21}$
Explanation
(a)
If line $4x - 3y + k = 0$ touches the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1$, then
$\frac{k}{3} = \sqrt{9 \times \left( \frac{4}{3} \right)^{2} + 5} = \pm \sqrt{21}$
$\Rightarrow \ k = \pm 3\sqrt{21}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.