ParabolaHardBloom L3
Question
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 :
Options
A.$\left( \frac{p}{2},p \right)$
B.$\left( \frac{p}{2}, - p \right)$
C.$\left( \frac{- p}{2},p \right)$
D.$\left( \frac{- p}{2},\frac{- p}{2} \right)$
Solution
Sol. [Key Concept: A circle centred at the focus and touching the directrix has radius equal to the focus–directrix distance; its meet with the parabola is a latus-rectum end $(\frac{p}{2}, \pm \ p)$.]
$AB$ is latus rectum of parabola
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