Question

The lines 2x - 3y + 7 = 0 and 4x - 6y - 5 = 0 are
tangent to the same circle. The radius of the circle
is--​

Answer 1

Answer:

2x + 3y - 9 = 0 and 4x + 6y + 19 =0 are parallel to each other. We can write the first one as 4x + 6y - 18 = 0

Now there is a standard formula for calculating the distance between two parallel lines y = mx+c1 and y=mx+c2:

d = (c1 - c2)/((1 + m^2)^0.5)

Here c1 = 18, c2 = -19 and m = -4/6

d therefore is = (18 + 19)/((1 + 16/36)^0.5)

d = 222/7.211 = 30.78. This is the diameter. Radius = d/2 = 15.4

Explanation: