JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let an ellipse with centre \((1,0)\) and latus rectum of length \(\frac{1}{2}\) have its major axis along \(x\)-axis. If its minor axis subtends an angle \(60^{\circ}\) at the foci, then the square of the sum of the lengths of its minor and major axes is equal to \(...........\).
- A \(9\)
- B \(8\)
- C \(7\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(9\)
Step-by-step Solution
Detailed explanation
\(\text { L.R. }=\frac{2 b^2}{a}=\frac{1}{2}\) \(4 b^2=a.......(i)\) \(\text { Ellipse } \frac{(x-1)^2}{a^2}+\frac{y^2}{b^2}=1\) \(m_{B_2 F_1}=\frac{1}{\sqrt{3}}\) \(\frac{b}{a}=\frac{1}{\sqrt{3}}\) \(3 b^2=a^2 e^2=a^2-b^2\) \(4 b^2=a^2........(ii)\)…
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