Q. The circle $x^{2} + y^{2} = 4x + 8y + 5$ intersects the line $3x - 4y = m$ at two distinct points, if
A) $- 85 < m < - 35$
B) $- 35 < m < 15$
C) $15 < m < 65$
D) $35 < m < 85$
Explanation
(b)
Centre of circle is (2, 4) and radius is 5. The line will intersect the circle at two distinct points, if the distance of (2, 4) from $3x - 4y = m$ is less than radius of the circle.
$ie,\ \ \ \left| \frac{6 - 16 - m}{5} \right| < 5$
$\Rightarrow \ - 25 < 10 + m < 25$
$\Rightarrow \ - 35 < m < 15$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.