TS EAMCET · Maths · Ellipse
\(a\) and \(b\) are the semi-major and semi-minor axes of an ellipse whose axes are along the coordinate axes. If its latus rectum is of length 4 units and the distance between its foci is \(4 \sqrt{2}\), then \(a^2+b^2=\)
- A 24
- B 18
- C 16
- D 12
Answer & Solution
Correct Answer
(A) 24
Step-by-step Solution
Detailed explanation
Length of latus rectum \(=\frac{2 b^2}{a}=4\) \(\Rightarrow b^2=2 a\) Distance between focii \(=2 a e=2 a \sqrt{1-\frac{b^2}{a^2}}=4 \sqrt{2}\) \(\Rightarrow 2 a \sqrt{1-\frac{2}{a}}=4 \sqrt{2} \Rightarrow 4 a^2\left(1-\frac{2}{a}\right)=32\)…
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