Find the equation of the circle which touches both the axes and the line `3x-4y+8=0` and lies in the third quadrant.

Explanation

Let ' a ' be the radius of the circle.


therefore centre of circle


`( -a,-a)`[because the circle touches both the axes and lies in the third quadrant]


Given that the line` 3 x-4 y+8=0 `touches the circle.


Therefore` 3 x-4 y+8=0 `is tangent to the circle.


As we know that the radius and a tangent to a circle are always perpendicular to each other.


therefore perpendicular distance from the centre of circle to the tangent = a units, i.e.,



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