AP EAMCET · Maths · Ellipse
If the normal drawn at the point \(P\left(\frac{\pi}{4}\right)\) on the ellipse \(x^2+4 y^2-4=0\) meets the ellipse again at \(\mathrm{Q}(\alpha, \beta)\), then \(\alpha=\)
- A \(\sqrt{2}\)
- B \(\frac{-23}{17 \sqrt{2}}\)
- C \(\frac{7 \sqrt{2}}{17}\)
- D \(\frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(C) \(\frac{7 \sqrt{2}}{17}\)
Step-by-step Solution
Detailed explanation
Ellipse: \(x^2+4y^2=4 \Rightarrow \frac{x^2}{4}+\frac{y^2}{1}=1 \Rightarrow a^2=4, b^2=1\). Point P: \(x_1=a\cos(\frac{\pi}{4}) = 2 \cdot \frac{1}{\sqrt{2}} = \sqrt{2}\). \(y_1=b\sin(\frac{\pi}{4}) = 1 \cdot \frac{1}{\sqrt{2}} = \frac{1}{\sqrt{2}}\). Normal equation at…
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