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. 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?