Consider a circle whose centre lies at the focus of the parabola and which touches…

MATHEMATICS · Multi correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Consider a circle whose centre lies at the focus of the parabola

y^2=2ax

and which touches the directrix of the parabola. Then points of intersection of the circle and the parabola are (1)

\left(\frac{a}{2},a\right)

(2)

\left(\frac{a}{2},-a\right)

(3)

\left(-\frac{a}{2},a\right)

(4)

\left(-\frac{a}{2},-a\right)