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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Coordinate Geometry
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Find the equation of asymptotes for the hyperbola $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$$=1$?

$\begin{array}{1 1}(a)\;\large\frac{x}{a}\pm \frac{y}{b}\normalsize=0\\(b)\;\large\frac{x^2}{a}\pm \frac{y^2}{b}\normalsize=0\\(c)\;\large\frac{x}{b}\pm \frac{y}{a}\normalsize=0\\(d)\;\text{None of these}\end{array}$

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Let $y=mx+c$ be an asymptote of the hyperbola $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$$=1$------(1)
Substituting y in (1) we get
$\large\frac{x^2}{a^2}-\frac{(mx+c)^2}{b^2}$$=1$
$(a^2m^2-b^2)x^2+2a^2mck+a^2(b^2+c^2)=0$------(2)
If the $y=mx+c$ is an asymptote to the given hyperbola then it touches the hyperbola at infinity,so both roots of (2) is infinity
Hence $a^2m^2-b^2=0$ and $-2a^2mc=0$
$m=\pm\large\frac{b}{a}$ and $c=0$
Substituting the value of m and c in $y=mx+c$ we get,
$y=\pm \large\frac{b}{a}$$x$
$\large\frac{x}{a}\pm \frac{y}{b}\normalsize=0$
Hence (a) is the correct answer.
answered Feb 10, 2014 by sreemathi.v
 

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