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  • Let an ellipse with centre (1,0) and latus rectum of length  have its major axis along x-ax

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° at the foci, then the square of the sum of the lengths of its minor and major axes is equal to ________

Option: 1

9


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} & \text { L.K. }=\frac{2 b^2}{a}=\frac{1}{2} \\ & 4 b^2=a \\ & \text { Elipse } \frac{(x-1)^2}{a^2}+\frac{y^2}{b^2}=1 \\ & m_{b_1 k_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 \\ & \text { From (i) and }(i i) \\ & a=a^2 \\ & \therefore a=1 \\ & b^2=\frac{1}{4} \\ & ((2 a)+(2 b))^2=9 \end{aligned}

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