# Find the eccentricity of an ellipse whose latus â€“ rectum is half of its minor axis.

$We\;need\;to\;find\;the\;eccentricity\;of\;an\;ellipse.\\*If\;latus-rectum\;is\; half\;of\;its\;minor\;axis\\*We\;know\;that\;the\;length\;of\;the\;semi-minor\; axis\;is\;b\;and\;the\;length\;of\;the\\*latus-rectum\;is\;\frac{2b^2}{a}.\\* \Rightarrow \frac{2b^2}{a}=b\\*\Rightarrow\;a=2b....eq(1)\\* By\;using\; the\;formula,\;We\;know\;that\;eccentricity\;of\;an\;ellipse\;is\;given\;as\\* \Rightarrow e=\sqrt{\frac{a^2-b^2}{a^2}}\\*From\;eq..(1)\\*\Rightarrow e=\sqrt{\frac{(2b)^2-b^2}{(2b)^2}}=\sqrt{\frac{4b^2-b^2}{4b^2}}= \sqrt{\frac{3b^2}{4b^2}}=\frac{\sqrt3}{2}\\*\therefore e=\frac{\sqrt3}{2}$

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