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 [IIT 1995]

\[\left( \frac{-p}{2},\ p \right)\]

\[\left( \frac{p}{2},\ p \right)\]

\[\left( \frac{p}{2},\ -p \right)\]

\[\left( \frac{-p}{2},\ p \right)\]

\[\left( \frac{-p}{2},\ -p \right)\]

Consider a circle with its centre lying on the focus of the parabola \

1.	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 [IIT 1995]
A.	\[\left( \frac{p}{2},\ p \right)\]
B.	\[\left( \frac{p}{2},\ -p \right)\]
C.	\[\left( \frac{-p}{2},\ p \right)\]
D.	\[\left( \frac{-p}{2},\ -p \right)\]
Answer» C. \[\left( \frac{-p}{2},\ p \right)\]

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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 [IIT 1995]

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