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Questions  >>  CBSE XI  >>  Math  >>  Conic Sections
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Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas : $5y^2-9x^2=36$

$\begin {array} {1 1} (A)\;Foci : ( 0, \pm 2\sqrt{14} / \sqrt{5} ), Vertices : ( 0, \pm 6 / \sqrt 5), e = \sqrt{14} / 3, Length \; of \: the \: latus\: rectum 4\sqrt 5 / 3 \\ (B)\;Foci : ( \pm 2\sqrt{14} / \sqrt{5} , 0), Vertices : ( \pm 6 / \sqrt 5, 0), e = \sqrt{14} / 3, Length \; of \: the \: latus\: rectum 4\sqrt 5 / 3 \\ (C)\;Foci : ( 2\sqrt{14} / 5, 0 ), Vertices : ( 6 / \sqrt 5, 0), e = \sqrt{14} / 3, Length \; of \: the \: latus\: rectum 4\sqrt 5 / 3 \\ (D)\;Foci : ( -\pm 2\sqrt{14} / \sqrt{5}, 0 ), Vertices : ( -6 / \sqrt 5, 0), e = \sqrt{14} / 3, Length \; of \: the \: latus\: rectum 4\sqrt 5 / 3 \end {array}$

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