Question

The combined equation of the asymptotes of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$..

• A. True
• B. False

Answer 1

The correct option is B

False

Let y=mx+c be an asymptotes of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

the abscissae of the points of intersection of y=mx+c and are the roots of equation

$\frac{x^2}{a^2}-\frac{(mx+c{)}^2}{b^2}=1$

$x^2(b^2-a^2{m}^2)-2a^{2}mcx-a^2(c^2+b^2)=0$ ......................(1)

if the line y=mx+c is a asymptote to the given hyperbola, then it touches the hyperbola at infinity.so,both the roots of equation must be infinity.

coefficient of $x^2=0$

$\Rightarrow b^2-a^2{m}^2=0$

$m=\pm \frac{b}{a}$

and $-2a^{2}mc=0$

$\Rightarrow c=0$