The equation of a circle of a circle which touches the line `x + y = 5` at the point `(-2, 7)` and cuts the circle `x^(2) + y^(2) + 4x -6y + 9 =0` orthogonally is

Options

A. `x^(2)+y^(2)+7x-11y+38=0`
B. `x^(2)+y^(2)+7x+11y+38=0`
C. `x^(2)+y^(2)+7x-11y-38=0`
D. `x^(2)+y^(2)-7x-11y+39=0`

Answer

A

Explanation

Let equation of circle `S-=x^(2)+y^(2)+2gx+2fy+c=0`
`(-2,7)` lies on the circle
`:." "-4g+14f+c=-53`……(i)
Equation of a line through (-2,7) and perpendicular to line `x+y=5` is
`y-7=1(x+2)`
`x-y+9=0`
Centre `(-g,-f)` lie on this line `-g+f+9=0`.........(ii)
Circle `S` and `S_(2)` are orthogonal
`:." "2g(2)+2f(-3)=c+9`
`4g-6f-c=9`..............(iii)
Solve equation (i) and (iii) `f=(-11)/2`
`g=7/2,c=38`
`:." "` Equation of circle `x^(2)+y^(2)+7x-11y+38=0`