Q. If the equation of tangent to the circle $x^{2} + y^{2} - 2x + 6y - 6 = 0$ parallel to $3x - 4y + 7 = 0$ is $3x - 4y + k = 0$, then the value of $k$ are
A) $5,\ - 35$
B) $- 5,\ 35$
C) $7,\ - 32$
D) $- 7,\ 32$
Explanation
(a)
The centre and radius of given circle are $(1,\ - 3)$ and 4 respectively
$\therefore$ Length of perpendicular from centre $(1,\ - 3)$ to $3x - 4y + k = 0$ is equal to radius 4
$\ \Rightarrow \ \ \left| \frac{3 + 12 + k}{\sqrt{9 + 16}} \right| = 4$
$\Rightarrow 15 + k = \pm 20$
$\Rightarrow \ \ k = 5,\ - 35$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.