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The equation of a circle which touches t...

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

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`

Text Solution

Verified by Experts

The correct Answer is:
A
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`
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