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Question

Let the equation of the circle which passes through the focus of the parabola x2=4y and touches it at the point (6,9) be x2+y2+mxny+27=0. Find nm1?

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Solution

Focus of the given parabola is (0,1)
Given circle x2+y2+mxny+27=0. passes through (0,1)
0+1+0n+27n=28
Also given circle passes through (6,9)
36+81+6m28×9+27=0m=18
nm1=9

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