TS EAMCET · Maths · Ellipse
If tangents are drawn to the ellipse \(x^2+2 y^2=2\), then the locus of the mid-points of the intercepts made by those tangents between the coordinate axes is
- A \(\frac{x^2}{2}+\frac{y^2}{4}=1\)
- B \(\frac{x^2}{4}+\frac{y^2}{2}=1\)
- C \(\frac{1}{2 x^2}+\frac{1}{4 y^2}=1\)
- D \(\frac{1}{4 x^2}+\frac{1}{2 y^2}=1\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2 x^2}+\frac{1}{4 y^2}=1\)
Step-by-step Solution
Detailed explanation
Given ellipse, \(x^2+2 y^2=2 \Rightarrow \frac{x^2}{2}+\frac{y^2}{1}=1\) Point \(P(\sqrt{2} \cos \theta, \sin \theta)\) lie in ellipse Tangent at \(P(\sqrt{2} \cos \theta, \sin \theta)\) on ellipse is, \(x \cos +\sqrt{2} \sin \theta y=\sqrt{2}\) intercept on line is,…
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