~~Show that the circles x^2+y^2-4x+4y+4=0 touches the coordinate axes If the points of contact are A and B, find - Maths - Straight Lines

Question

~~Show that the circles x^2+y^2-4x+4y+4=0 touches the coordinate
axes If the points of contact are A and B, find the equation of the
circle which passes through A,B and the origin

Brijendra Pal · Accepted Answer

Hi, The equation of the cirle is x2+y2-4x+4y+4=0 x2-4x+4+y2+4y+4=4x-22+y+22=22So centre is 2,-2 and radius is = 2 Now if it touches the axis then 2,0, 0,-2 will satisfy it and that is true
 You may check by putting Also drawing them you may see the same
 A2,0,B 0,-2 and O0,0So one method is to let equation of circle as x-a2+y-b2= r2 and put these values of x, y but second method is easyNow you know that AB will be a diamter as angle in semicircle is 90 degree so equation of the circle can be find out using concept of diameter AB will be a diameter So equation will be x-2x-0+y-0y+2=0 x2-2x+y2+2y= 0 Regards

~~Show that the circles x^2+y^2-4x+4y+4=0 touches the coordinate axes. If the points of contact are A and B, find the equation of the circle which passes through A,B and the origin.