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10-2. Parabola, Ellipse, Hyperbola
normal
Length of latus rectum of hyperbola $\frac{{{x^2}}}{{{{\cos }^2}\alpha }} - \frac{{{y^2}}}{{{{\sin }^2}\alpha }} = 4\,is\,\left( {\alpha \ne \frac{{n\pi }}{2},n \in I} \right)$
A
$2\left| {\frac{{1 - \cos 2\alpha }}{{\cos \alpha }}} \right|$
B
$\left| {\frac{{1 + \cos 2\alpha }}{{\sin \alpha }}} \right|$
C
$2\left| {\frac{{1 + \cos 2\alpha }}{{\sin \alpha }}} \right|$
D
$\left| {\frac{{1 - \cos 2\alpha }}{{\cos \alpha }}} \right|$
Solution
Use length of $LR\, = \frac{{2{b^2}}}{a}$
$ = \left| {2\left( {\frac{{4\,{{\sin }^2}\,\alpha }}{{2\,\cos \,\alpha }}} \right)} \right| = \left| {\frac{{2(1 – \cos \,2\alpha )}}{{\cos \,\alpha }}} \right|$
Standard 11
Mathematics
