If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then find the radius of the circle.
Slope of 3x−4y+4=,0is43
Slope of 6x−8y−7=0 is 86=43
Slope of 3x−4y+4−0 and 6x−8y−7=0 are same.
Hence two lines are parallel and are shown in figure.
Rewriting 6x−8y−7=0, we get
3x−4y−72=0
Perpendicular distance between two lines
=∣∣∣4+72√9+16∣∣∣
=∣∣1510∣∣
=32 units.