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10-2. Parabola, Ellipse, Hyperbola
easy
જો ઉપવલયનો નાભિલંબ તેની ગૌણ અક્ષ કરતાં અડધો હોય, તો તેની ઉન્કેન્દ્રિતા ...
A
$\frac{3}{2}$
B
$\frac{2}{3}$
C
$\frac{{\sqrt 3 }}{2}$
D
$\frac{{\sqrt 2 }}{3}$
Solution
આપેલ મુજબ $\,\frac{{2{b^2}}}{a}\,\, = \,\,b$
$ \Rightarrow \,\,2b\,\, = \,\,a\,\, $
$\Rightarrow \,\,4{b^2}\,\, = \,\,{a^2}\,\, $
$\Rightarrow \,\,4{a^2}\,\,\left( {1\,\, – \,\,{e^2}} \right)\,\, = \,\,{a^2}\,\, $
$\Rightarrow \,\,1\,\, – \,\,{e^2}\,\, = \,\,1/4\,\,$
$\,\,\therefore \,\,\,e\,\, = \,\,\sqrt 3 /2$
Standard 11
Mathematics
