A circle touches the parabola at a point . It also passes through the focus of the parabola and intersects its horizontal axis at . If is , and the equation of the circle can be written as then find .
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Ans. 5
The circle has a center at C(ka,0), and radius r=4a. Since the point C, F and Q are on the x-axis and the line drawn through them are the diameter of the circle, (<FPQ = 90 ), then we can find the the radius r = (ka – a) = 4a, then k =5