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Find the equation of the circle having r...

Find the equation of the circle having radius 5 and which touches line `3x+4y-11=0` at point (1, 2).

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As shown in the figure, the two circles touch the line `3x+4y-11=0` at point (P(1,2).
`:. ` Centre lies on the line perpendicular to the tangent at P at distance 5 from it on either side.

Slope of given tangent line is `-(3)/(4)`
Thus, the slope of CP is `(4)/(3)`.
`:. tan theta=(4)/(3)`
`:. `Centre, `C-=(1+-5 cos theta, 2+- 5 sin theta)`
`:. C-= (1+-5(3)/(5),2+-5(4)/(5))`
`:. C-= (4,6)` or `(-2 , -2)`
Therefore, equations of circles are
`(x-4)^(2)+(y-6)^(2)=25`
or `(x+2)^(2)+(y+2)^(2)=25`
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