AP EAMCET · Maths · Ellipse
Let \(\mathrm{C}\) be the centre of an ellipse and \(\mathrm{PQ}\) be a chord of it with \(\lfloor\mathrm{PCQ}=90^{\circ}\). If \(\mathrm{R}\) is the point of intersection of the tangents to the ellipse at \(P\) and \(Q\) then \(R\) lies on
- A a straight line
- B a parabola
- C an ellipse
- D a hyperbola
Answer & Solution
Correct Answer
(C) an ellipse
Step-by-step Solution
Detailed explanation
Let the ellipse be \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\). Let R be \((h, k)\). The equation of the chord PQ is \(\frac{hx}{a^2} + \frac{ky}{b^2} = 1\). The equation of the pair of lines CP and CQ is obtained by homogenizing the ellipse equation using the chord equation:…
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