Q. The equations of the tangents to circle $x^{2} + y^{2} - 6x + 4y - 12 = 0$, which are parallel to line $4x + 3y + 15$are
A) $4x + 3y + 11 = 0$ and $4x + 3y + 8 = 0$
B) $4x + 3y - 9 = 0$ and $4x + 3y + 7 = 0$
C) $4x + 3y + 19 = 0$ and $4x + 3y - 31 = 0$
D) $4x + 3y - 10 = 0$ and $4x + 3y + 12 = 0$
Explanation
(c)
The centre and radius of given circle are $(3,\ - 2)$ and 5 respectively
The equation of a line parallel to $4x + 3y + 5 = 0$ is $4x + 3y + \lambda = 0$
$\therefore\ \ \ \left| \frac{4 \times 3 + 3 \times ( - 2) + \lambda}{\sqrt{4^{2} + 3^{2}}} \right| = 5$
$\Rightarrow \ \ \ \lambda = 19,\ - 31$
$\therefore$ Equation of tangents are
$4x + 3y + 19 = 0$ and $4x + 3y - 31 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.