find the equation of a circle which touches both the axes and the line 3x - 4y +8=0 and lies - Maths - Conic Sections

Question

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

Anuradha Sharma · Accepted Answer

The equation of a circlein the third quadrant touching the coordinate axis wuth center -a,-a and radius a is , x--a2+y--a2=a2x2+y2+2ax+2ay+a2=0And we know that distance from center to the tangent 3x-4y+8=0, is radius so
 3-a-4-a+89+16=aSolving we get, a+8=5ataking positive value only as at negative value a is negative
a+8=5a4a=8a=2Hence the required equation is, x2+y2+4x+4y+4=0

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