The line `2x -y +6= 0` meets the circle `x^2+y^2 -2y-9 =0` at A and B. Find the equation of the circle on AB as diameter.

Explanation

The equation of the line `x=frac{y-6}{2}.`


Put the value of x in the equation of the circle `= (frac{y-6}{2})^{2}+y^{2}-2 y-9=0`


`Rightarrow(y-6)^{2}+4 y^{2}-8 y-36=0 `


`Rightarrow y^{2}+36-12 y+4 y^{2}-8 y-36=0 `


`Rightarrow 5 y^{2}-20 y=0`


`Rightarrow y^{2}-4 y=0 `


`Rightarrow y(y-4)=0 `


`Rightarrow y=0,4`


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