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 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.

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