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A circle of radius 5 is tangent to the l...

A circle of radius 5 is tangent to the line `4x-3y=18` at M(3, -2) and lies above the line. The equation of the circle is

A

`x^(2)+y^(2) -6x +4y - 12 = 0`

B

`x^(2) +y^(2) +2x - 2y - 3 =0`

C

`x^(2) +y^(2) +2x -2y - 23 = 0`

D

`x^(2) +y^(2) +6x +4y -12 = 0`

Text Solution

Verified by Experts

The correct Answer is:
C

Let `(x-3)/(cos theta) =(y+2)/(sin theta) =5`, where `tan theta = (-3)/(4)`
`rArr x = 5 cos theta +3`
and `y = 5 sin theta -2`
we have, `cos theta =(-4)/(5)` and `sin theta = (3)/(5)`
`:. x =-1` and `y =1`
`rArr` centre `-= (-1,1)`
Hence, required equation of circle is
`(x+1)^(2) +(y-1)^(2) -25`
`rArr x^(2)+y^(2) +2x -2y -23 =0`
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