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Question

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

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Solution

Slope of 3x4y+4=,0is43
Slope of 6x8y7=0 is 86=43
Slope of 3x4y+40 and 6x8y7=0 are same.
Hence two lines are parallel and are shown in figure.

Rewriting 6x8y7=0, we get
3x4y72=0
Perpendicular distance between two lines
=4+729+16

=1510

=32 units.


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