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CGP EDU Academic Team
Published on: August 14, 2026
Consider a circle with its centre lying on the focus of the parabola y 2 = 2px such that it touches the directrix of the parabola. Then, a point of intersection of the circle and the parabola is
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(a, b)
Focus of parabola y 2 = 2px is (p/2, 0) ...(i)
∴ ∴ Radius of circle whose centre is (p/2, 0) and touching x+(p/2) = 0 is p.
Equation of circle is 
2 = p 2 ...(ii)
From (i) and (ii), we get the point of intersection (p/2, p), (p/2, -p).
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