A rectangular hyperbola of latus rectum 2 units passes through (0, 0) and has (1, 0) as its one

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10-2. Parabola, Ellipse, Hyperbola

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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

$4x^2 + y^2 = 1$

B

$x^2 + y^2 = 9$

C

$x^2 -y^2 = 1$

D

$4x^2 -y^2 = 1$

Solution

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 $x^{2}+y^{2}=9.$

Standard 11

Mathematics

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