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  • Find the equation of a circle which touches both the axes and the line 3x minus 4y plus 8 equal to 0 and lies in the third quadrant.

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

Answers (1)

Since circle touches both the axes, its centre is C(-a, -a) and radius is a

Also, circle touches the line 3x-4y+8=0

Distance from centre C to this line is radius of the circle

Radius of circle, a=\left |\frac{-3a+4a+8}{\sqrt{9+16}} \right |=\left | \frac{a+8}{5} \right |

\left | \frac{a+8}{5} \right |=\pm a

a=2 or a=-4/3

a=2

Equation of required circle

(x+2)2+(y+2)2=22

x2+y2+4x+4y+4=0

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