TS EAMCET · Maths · Parabola
If a circle with its centre at the focus of the parabola \(y^2=2 p x\) is such that it touches the directrix of the parabola, then a point of intersection of the circle and the parabola is
- A \(\left(\frac{p}{2}, 2 p\right)\)
- B \(\left(\frac{-p}{2}, p\right)\)
- C \(\left(\frac{p}{2},-p\right)\)
- D \(\left(\frac{-p}{2},-p\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{p}{2},-p\right)\)
Step-by-step Solution
Detailed explanation
Equation of given parabola is \(y^2=2 p x\) having focus \(F\left(\frac{p}{2}, 0\right)\) and equation of directrix is \(x+\frac{p}{2}=0\), so equation of circle having centre \(\left(\frac{p}{2}, 0\right)\) and radius \(r=p\), because the circle touches the directrix of the…
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