WBJEE · Maths · Ellipse
On the ellipse \(4 x^{2}+9 y^{2}=1\), the points at which the tangents are parallel to the line \(8 x=9 y,\) are
- A \(\left(\frac{2}{5}, \frac{1}{5}\right)\)
- B \(\left(-\frac{2}{5}, \frac{1}{5}\right)\)
- C \(\left(-\frac{2}{5},-\frac{1}{5}\right)\)
- D \(\left(\frac{2}{5},-\frac{1}{5}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(\frac{2}{5},-\frac{1}{5}\right)\)
Step-by-step Solution
Detailed explanation
Given equation of ellipse is \[ 4 x^{2}+9 y^{2}=1 \] On differentiating. we get \(\Rightarrow \quad 8 x+18 yy'=0\) \(\Rightarrow \quad y'=\frac{-8 x}{18 y}=m\) Also, \(8 x=9 y \quad\) [equation of line] On differentiating. we got \(\Rightarrow \quad 8=9 y^{\prime}\)…
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