Geo4.95

Find the equation of the circle whose radius is 5units and which touches the circle  at the point (5,5).

equation of the tangent at(5,5) to the circle is

$x(5)+y(5)-(x+5)-2(y+5)-20=0\,$

$4x+3y-35=0\,$

Equation of the circle touching the the circle at (5,5) is

$x^2+y^2-2x-4y-20+k(4x+3y-35)=0\,$

$x^2+y^2-2x(1-2k)-y(4-3k)-20-5k=0\,$

Given radius is 5.

Hence

$4(1-2k)^2+(4-3k)^2+4(20+5k)=4(25)\,$

$4(1+4k^2-4k)+16+9k^2-24k+80+20k=100\,$

$k^2+4k=0,k=0,-4\,$

Therefore,the required circle is

$x^2+y^2-2x-4y-20-4(4x+3y-35)=0\,$

$x^2+y^2-18x-16y+120=0\,$