AP EAMCET · Maths · Parabola
A circle is drawn with its centre at the focus of the parabola \(y^2=2 p x\) such that it touches the directrix of the parabola. Then a point of intersection of the circle and the parabola is
- A \((2 p, 2 p)\)
- B \(\left(\frac{\mathrm{p}}{2},-\mathrm{p}\right)\)
- C \((2 p,-2 p)\)
- D \((p, \sqrt{2} p)\)
Answer & Solution
Correct Answer
(B) \(\left(\frac{\mathrm{p}}{2},-\mathrm{p}\right)\)
Step-by-step Solution
Detailed explanation
Focus: \(\left(\frac{p}{2}, 0\right)\) Directrix: \(x = -\frac{p}{2}\) Radius: \(r = \left|\frac{p}{2} - \left(-\frac{p}{2}\right)\right| = p\) Circle: \(\left(x - \frac{p}{2}\right)^2 + y^2 = p^2\) Substitute \(y^2 = 2px\): \(\left(x - \frac{p}{2}\right)^2 + 2px = p^2\)…
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