WBJEE · Maths · Ellipse
Consider a tangent to the ellipse \(\frac{x^{2}}{2}+\frac{y^{2}}{1}=1\) at any point. The locus of the midpoint of the portion intercepted between the axes is
- A \(\frac{x^{2}}{2}+\frac{y^{2}}{4}=1\)
- B \(\frac{x^{2}}{4}+\frac{y^{2}}{2}=1\)
- C \(\frac{1}{3 x^{2}}+\frac{1}{4 y^{2}}=1\)
- 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
Hint: Tangent at \(\mathrm{P}\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)\) \(\frac{x x_{1}}{2}+\frac{y y_{1}}{1}=1\) Let mid point of intercept be \(\mathrm{P}(\mathrm{h}, \mathrm{k})\) \(\mathrm{h}=\frac{1}{\mathrm{x}_{1}}, \mathrm{k}=\frac{1}{2 \mathrm{y}_{1}}\) or…
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