Let P is a point on hyperbola x^2 -y^2 = 4 , which is at minimum distance from (0,-1) then distance

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10-2. Parabola, Ellipse, Hyperbola

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Let $P$ is a point on hyperbola $x^2 -y^2 = 4$ , which is at minimum distance from $(0,-1)$ then distance of $P$ from $x-$ axis is

A

$0$

B

$\frac{1}{2}$

C

$1$

D

$\sqrt 2 $

Solution

$\mathrm{PQ}=\sqrt{\mathrm{x}^{2}+(\mathrm{y}+1)^{2}}$

$=\sqrt{y^{2}+4+y^{2}+2 y+1}$

$=\sqrt{2\left(\mathrm{y}+\frac{1}{2}\right)^{2}+\frac{9}{2}}$

$\mathrm{PQ}$ is minimum if $\mathrm{y}=-\frac{1}{2}$

Standard 11

Mathematics

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