AP EAMCET · Maths · Ellipse
If tangents are drawn to the ellipse \(x^2+2 y^2=2\), then the locus of the midpoints of the intercepts made by the tangents between the coordinate axes is
- A \(\frac{x^2}{4}+\frac{y^2}{2}=1\)
- B \(\frac{x^2}{2}+\frac{y^2}{4}=1\)
- C \(\frac{1}{4 x^2}+\frac{1}{2 y^2}=1\)
- D \(\frac{1}{2 x^2}+\frac{1}{4 y^2}=1\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{2 x^2}+\frac{1}{4 y^2}=1\)
Step-by-step Solution
Detailed explanation
Equation of ellipse: \(\frac{x^2}{2}+\frac{y^2}{1}=1\) Tangent at \((x_1, y_1)\): \(\frac{x x_1}{2}+\frac{y y_1}{1}=1\) Intercepts: \(A = \left(\frac{2}{x_1}, 0\right)\), \(B = \left(0, \frac{1}{y_1}\right)\) Midpoint \((h, k)\): \(h = \frac{1}{x_1}\), \(k = \frac{1}{2y_1}\)…
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