TS EAMCET · Maths · Ellipse
A tangent drawn at a point on the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\) cuts the \(X\)-axis at point \(A\). If \(A^{\prime}\) be the image of \(A\) with respect to the line \(y=x\), then the circle with \(A A^{\prime}\) as its diameter passes through the fixed point
- A \((0,-4)\)
- B \((0,4)\)
- C \((0,0)\)
- D \((1,1)\)
Answer & Solution
Correct Answer
(C) \((0,0)\)
Step-by-step Solution
Detailed explanation
Given equation of ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\) Let \(P(5 \cos \theta, 4 \sin \theta)\) be a point on \(16 x^2+25 y^2=400\). The equation of the tangent at \(P\) is \(4 x \cos \theta+5 y \sin \theta=20\) This meets the coordinate axes at \(A(5 \sec \theta, 0)\) and…
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