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 \(\angle \mathrm{AOB}=\)
- A \(\frac{\pi}{4}\)
- B \(\operatorname{Tan}^{-1} 2\)
- C \(\operatorname{Tan}^{-1}\left(\frac{1}{2}\right)\)
- D \(\frac{\pi}{6}\)
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, \(a=1, 2h=2 \Rightarrow h=1, b=0\).…
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