find the equation of circle
if the line 2x - y +1 = 0 touches the circle at the point (2,5) and the center of the circle lies on the line x+y -9 =0

Question

find the equation  of circle
if the line 2x - y +1 = 0 touches the circle at the point (2,5) and the center of the circle lies on the line x+y -9 =0

experimentx · Answer

let the equation of circle by (x-a)^2+(y-b)^2 = r^2,
put x,y = 2,5 and get equation on a,b ... put a,b in x+y -9 =0  and solve them.

anonymous · Answer

(2-a)^2+(5-b)^2 = r^2
4+ a^2-4a+25-10b+b^2 = r^2
 a^2+b^2-4a-10b+29=r^2

experimentx · Answer

woops ... that doesn't solve it all. add the condition of perpendicularity.

experimentx · Answer

a+b -9 =0 

and the condition of perpendicularity, solve of radius joining center to (2,5) times slope of the former line = -1

anonymous · Answer

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experimentx · Answer

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