Consider a circle with its centre lying on the focus of the parabola, y 2 = 2 px (p > 0)…

Mathematics · JEE Advanced · NTA ExamsCo-ordinate Geometry

Consider a circle with its centre lying on the focus of the parabola, y2 = 2 px (p > 0) such that it touches the directrix of the parabola. Then a point of intersection of the circle & the parabola is :
  1. \(\left(\frac{\mathrm{p}}{2}, \mathrm{p}\right)\)
  2. \(\left(\frac{\mathrm{p}}{2},-\mathrm{p}\right)\)
  3. \(\left(-\frac{\mathrm{p}}{2}, \mathrm{p}\right)\)
  4. \(\left(-\frac{\mathrm{p}}{2},-\mathrm{p}\right)\)

Answer

(A) ( p 2 , p ), (B) ( p 2 ,- p )

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