TS EAMCET · Maths · Ellipse
Let P be a point on the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\) and let the perpendicular drawn through P to the major axis meet its auxiliary circle at Q. If the normals drawn at P and Q to the ellipse and the auxiliary circle respectively meet in R, then the equation of the locus of \(R\) is
- A \(x^2+y^2=5\)
- B \(x^2+y^2=13\)
- C \(x^2+y^2=25\)
- D \(x^2+y^2=1\)
Answer & Solution
Correct Answer
(C) \(x^2+y^2=25\)
Step-by-step Solution
Detailed explanation
Let \(P=(3\cos\theta, 2\sin\theta)\) and \(Q=(3\cos\theta, 3\sin\theta)\). Normal at \(P\) to the ellipse: \(3x\sec\theta - 2y\csc\theta = 3^2-2^2 = 5\) Normal at \(Q\) to the circle: \(y = x\tan\theta \Rightarrow x\sin\theta - y\cos\theta = 0\) Substitute \(y=x\tan\theta\) into…
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