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TS EAMCET · Maths · Ellipse

The locus of the mid points of the intercepted portion of the tangents by the coordinate axes, which are drawn to the ellipse \(x^2+2 y^2=2\) is

  1. A \(\frac{1}{2 x^2}+\frac{1}{4 y^2}=1\)
  2. B \(\frac{1}{4 x^2}+\frac{1}{2 y^2}=1\)
  3. C \(\frac{x^2}{2}+\frac{y^2}{4}=1\)
  4. D \(\frac{x^2}{4}+\frac{y^2}{2}=1\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{1}{2 x^2}+\frac{1}{4 y^2}=1\)

Step-by-step Solution

Detailed explanation

\[ \frac{x^2}{2}+\frac{y^2}{1}=1 \Rightarrow \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] Equation of tangent at \(P(a \cos \theta, b \sin \theta)\)…