A rectangular hyperbola of latus rectum 2 units passes through (0… - Vidyadip

MCQ

A rectangular hyperbola of latus rectum $2$ units passes through $(0, 0)$ and has $(1, 0)$ as its one focus. The other focus lies on the curve -

A
$4x^2 + y^2 = 1$
✓
$x^2 + y^2 = 9$
C
$x^2 -y^2 = 1$
D
$4x^2 -y^2 = 1$

✓

Answer

Correct option: B.

$x^2 + y^2 = 9$

b
We have $\left|\mathrm{PS}_{1}-\mathrm{PS}_{2}\right|=2 \mathrm{a}.$

$\Rightarrow \quad|\sqrt{\mathrm{h}^{2}+\mathrm{k}^{2}}-1|=2.$

$\therefore $ Other focus lie on $x^{2}+y^{2}=9.$

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