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# Find the equation of asymptotes for the hyperbola $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$$=1? \begin{array}{1 1}(a)\;\large\frac{x}{a}\pm \frac{y}{b}\normalsize=0\\(b)\;\large\frac{x^2}{a}\pm \frac{y^2}{b}\normalsize=0\\(c)\;\large\frac{x}{b}\pm \frac{y}{a}\normalsize=0\\(d)\;\text{None of these}\end{array} Can you answer this question? ## 1 Answer 0 votes Let y=mx+c be an asymptote of the hyperbola \large\frac{x^2}{a^2}-\frac{y^2}{b^2}$$=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.