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A circle cuts the parabola y^2=4ax at ri...

A circle cuts the parabola `y^2=4ax` at right angles and passes through the focus , show that its centre lies on the curve `y^2(a+2x)=a(a+3x)^2`.

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The correct Answer is:
`y^2(a+2x)=a(a+3x)^2`.
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