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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
Given equation are 3x – 4y + 4 = 0
And 6x – 8y – 7 = 0
⇒ `3x - 4y - 7/2` = 0
Since `3/6 = (-4)/(-8) = 1/2` then the lines are parallel.
So, the distance between the parallel lines
= `|(c_1 - c_2)/sqrt(a^2 + b^2)|`
= `|(4 + 7/2)/sqrt((3)^2 + (-4)^2)|`
= `|(15/2)/5|`
= `3/2`
Diameter = `3/2`
∴ Radius = `3/4`.
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