Conic Sections Question 450
Question: The coordinates of the foci of the rectangular hyperbola $ xy=c^{2} $ are
Options:
A) $ (\pm c,\ \pm c) $
B) $ (\pm c\sqrt{2},\ \pm c\sqrt{2}) $
C) $ ( \pm \frac{c}{\sqrt{2}},\ \pm \frac{c}{\sqrt{2}} ) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ 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}) $
Note: Students should remember this question as a fact.
BETA
