- Home
- Standard 11
- Mathematics
10-2. Parabola, Ellipse, Hyperbola
medium
The coordinates of the foci of the rectangular hyperbola $xy = {c^2}$ are
A
$( \pm c,\; \pm c)$
B
$( \pm c\sqrt 2 ,\; \pm c\sqrt 2 )$
C
$\left( { \pm \frac{c}{{\sqrt 2 }},\; \pm \frac{c}{{\sqrt 2 }}} \right)$
D
None of these
Solution
(b) $xy = {c^2}$ as ${c^2} = \frac{{{a^2}}}{2}$.
Here, co-ordinates of focus are
$(ae\cos 45^\circ ,\,ae\sin 45^\circ ) \equiv (c\sqrt 2 ,c\sqrt 2 )$,
$\{ \because e = \sqrt 2 $,$a = c\sqrt 2 \} $
Similarly other focus is $( – c\sqrt 2 , – c\sqrt 2 )$
Standard 11
Mathematics
