Question

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

Options

• `sqrt3/5`

• `17/(6sqrt5)`

• `(2sqrt5)/3`

• `17/(3sqrt5)`

Answer 1

If 2x - 4y = 9 and 6x - 12y + 7 = 0 are the tangents of same circle, then its radius will be `underline(17/(6sqrt5))`.

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 `34/(3 xx 2sqrt5) = 17/(3sqrt5)`  

∴ radius = `17/(6sqrt5)`