First slide

Definition of a circle

Question

If $2 x - 4 y = 9$ and $6 x - 12 y + 7 = 0$ are parallel tangents to circle, then radius of the circle, is

Moderate

A

$\frac{\sqrt{3}}{5}$
B

$\frac{17}{6 \sqrt{5}}$
C

$\frac{\sqrt{2}}{3}$
D

$\frac{17}{3 \sqrt{5}}$

Solution

The equations of two tangents are $2 x - 4 y - 9 = 1$ and $6 x - 12 y + 7 = 0$ . Clearly, these are parallel. The distance between these lines is
$|\frac{- 9 - 7}{\sqrt{4 + 16}}| = \frac{17}{3 \sqrt{5}}$ $[Using : d = \frac{|c_{1} - c_{2}|}{\sqrt{a^{2} + b^{2}}}]$
$∴$ Radius of the circle $= \frac{1}{2} \times \frac{17}{3 \sqrt{5}} = \frac{17}{6 \sqrt{5}}$

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