Q. If $2x - 4y = 9$ and $6x - 12y + 7 = 0$ are common tangents to the circle, then radius of the circle is
A) $\frac{\sqrt{3}}{5}$
B) $\frac{17}{6\sqrt{5}}$
C) $\frac{\sqrt{2}}{3}$
D) $\frac{17}{3\sqrt{5\ }}$
Explanation
(b)
Given common tangents are $2x - 4y - 9 = 0$ and $2x - 4y + \frac{7}{3} = 0$ which are parallel
$\therefore$ Diameter=distance between tangents
= distance between parallel lines
$= \frac{|c_{1} - c_{2}|}{\sqrt{a^{2} + b^{2}}} = \frac{\left| - 9 - \frac{7}{3} \right|}{\sqrt{2^{2} + (4)^{2}}}$
$\Rightarrow \ \ \ d = \frac{34}{3.2\sqrt{5}}$
$\therefore$ Radius$= \frac{17}{6\sqrt{5}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.