I'm doing a question in my book on conics where there is a circle cutting through a parabola. There are three points S - the focus P - a point on the parabola and Q - the point where the tangent at P meets the directrix.(adsbygoogle = window.adsbygoogle || []).push({});

The focus is at S[1,0] and the dirextrix is x=-1

point P is [t^2, 2t] and point Q is [-1, (t^2 -1)/t]

The question asks you to find the circle on which all three points lie.

I said that the equation of the circle would be (x-a)^2 + (y-b)^2=c^2

I put in the values of X and Y for each of the coordinates to get three expressions which are all equal to c^2 and then equated coefficients to get the values of a, b, and c. I thought this seemed obvious but my value for a keeps coming out as 1, which is wrong.

Can anyone see any other solution?

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# Homework Help: from a question on conics

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