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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 \(\alpha=\)

  1. A \(\sqrt{2}\)
  2. B \(\frac{-23}{17 \sqrt{2}}\)
  3. C \(\frac{7 \sqrt{2}}{17}\)
  4. D \(\frac{1}{\sqrt{2}}\)
Verified Solution

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…