AP EAMCET · Maths · Ellipse
If \(\alpha, \beta\) are the eccentric angles of the extremities of a focal chord (other than the major axis) of the ellipse \(x^2+4 y^2=4\) then \(\sqrt{3} \cos \frac{\alpha+\beta}{2}=\)
- A \(2 \cos \frac{\alpha-\beta}{2}\)
- B \(2 \sin \frac{\alpha-\beta}{2}\)
- C \(2 \sec \frac{\alpha+\beta}{2}\)
- D \(2 \sin \frac{\alpha+\beta}{2}\)
Answer & Solution
Correct Answer
(A) \(2 \cos \frac{\alpha-\beta}{2}\)
Step-by-step Solution
Detailed explanation
Ellipse: \(x^2+4 y^2=4 \Rightarrow \frac{x^2}{4} + \frac{y^2}{1} = 1 \Rightarrow a=2, b=1\) Eccentricity: \(e^2 = 1 - \frac{b^2}{a^2} = 1 - \frac{1}{4} = \frac{3}{4} \Rightarrow e = \frac{\sqrt{3}}{2}\) Condition for a focal chord:…
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