Question

If 2x - 4y = 9 and 6x - 12y + 7 = 0 are the tangents of same circle, then its radius will be ______ 

विकल्प

• ${\displaystyle \frac{\sqrt{3}}{5}}$

• ${\displaystyle \frac{17}{6\sqrt{5}}}$

• ${\displaystyle \frac{2\sqrt{5}}{3}}$

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

Answer 1

If 2x - 4y = 9 and 6x - 12y + 7 = 0 are the tangents of same circle, then its radius will be ${\displaystyle \underline{\frac{17}{6\sqrt{5}}}}$.

Explanation:

The diameter of the circle is perpendicular distance between the parallel lines (tangents)

2x - 4y - 9 = 0 and 6x - 12y + 7 = 0 and so it is equal to ${\displaystyle \frac{34}{3\times 2\sqrt{5}}=\frac{17}{3\sqrt{5}}}$  

∴ radius = ${\displaystyle \frac{17}{6\sqrt{5}}}$