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If the lines 3x-4y+4=0 and 6x-8y-7=0 are...

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

Text Solution

Verified by Experts

The correct Answer is:
`(3)/(4)`
Since, 3x - 4y + 4 =0 and `3x -4y-(7)/(2)=0` are two parallel tangents, Thus, diameter between them is diameter circle.
`rArr Diameter = (|4+(4)/(2)|)/(sqrt(3^(2)+4^(2)))=(15)/(2.5)=(3)/(2)`
and radius` = (3)/(4)`
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Knowledge Check

  • If the lines 3x-4y+4=0and6x-8y-7=0 are tangents to a circle ,then find the radius of the circle .

    A
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  • The lines 3x - 4y+4=0 and 3x - 4y -5=0 are tangents to the same circle. The radius of this circle is

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    `9//10`
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