Question

If the line `2x-y+1=0` touches the circle at the point `(2,5)` and the centre of the circle lies in the line `x+y-9=0.` Find the equation of the circle.

Answer 1

`2x-y+1=0`
Equation of Normal
`Y-Y_1=m(x-x_1)`
`Y-S=-1/2(x-2)`
`Y-S=-1/2x+1`
`2y-10+x-1=0`
`2y+x-11=0`
Equation of number.
`r=sqrt((7-2)^2+(9-5)^2)=sqrt34`
Equation of line
`(x-7)^2+(y-2)^2=34`.