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

Answer 1

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.

Answer 2

(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

Answer 3

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

Answer 4

a+b -9 =0

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

Answer 5

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