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AP EAMCET · Maths · Ellipse

The equation of a chord \(A B\) of an ellipse \(2 x^2+y^2=1\) is \(x-y+1=0\). If 0 is the origin, then \(\angle \mathrm{AOB}=\)

  1. A \(\frac{\pi}{4}\)
  2. B \(\operatorname{Tan}^{-1} 2\)
  3. C \(\operatorname{Tan}^{-1}\left(\frac{1}{2}\right)\)
  4. D \(\frac{\pi}{6}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\operatorname{Tan}^{-1} 2\)

Step-by-step Solution

Detailed explanation

Homogenize \(2 x^2+y^2=1\) using \(y-x=1\): \(2x^2 + y^2 = (y-x)^2\) \(2x^2 + y^2 = y^2 - 2xy + x^2\) \(x^2 + 2xy = 0\) For \(ax^2+2hxy+by^2=0\), \(\tan \theta = \frac{2 \sqrt{h^2-ab}}{|a+b|}\). Here, \(a=1, 2h=2 \Rightarrow h=1, b=0\).…