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If the tangent at (3,-4) to the circle ...

If the tangent at `(3,-4)` to the circle `x^2 +y^2 -4x + 2y-5 =0` cuts the circle `x^2 +y^2+16x + 2y +10=0` in A and B then the midpoint of AB is

Text Solution

Verified by Experts

The correct Answer is:
`(-6,-7)`
Equation of tangent to circle `x^(2)+y^(2)-4x+2y-5=0` at point (3,-4) is
`3x-4y-2(x+3)=(y-4)-5=0`
or `x-3y-15=0` (1)

Center of the second circle is `C(-8,-1)`.
Slope of CM is `'-3'`
Equation of CM is `y+1= -3 (x+8)`
or `3x+y+25=0` (2)
Solving (1) and (2), we get `M -= (-6,-7)`
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