If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then radius of the circle is

Question

If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then radius of the circle is (A)  (3/4) (B)  (2/3) (C)  (1/4) (D)  (5/2)

Tardigrade Admin · Accepted Answer

The diameter of the circle is perpendicular distance between the parallel lines (tangents) 3x - 4y + 4 = 0 and (4/√9+16)+(7/2/√9+16)=(3/2). Hence radius is (3/4).

Q. If the lines $3 x - 4 y + 4 = 0$ and $6 x - 8 y - 7 = 0$ are tangents to a circle, then radius of the circle is

$\frac{3}{4}$

$\frac{2}{3}$

$\frac{1}{4}$

$\frac{5}{2}$

The diameter of the circle is perpendicular distance between the parallel lines (tangents)
$3 x - 4 y + 4 = 0$ and
$\frac{4}{9 + 16} + \frac{7/2}{9 + 16} = \frac{3}{2}$ . Hence radius is $\frac{3}{4} .$

Q. If the lines 3x−4y+4=0 and 6x−8y−7=0 are tangents to a circle, then radius of the circle is

43​

32​

41​

25​