Question

What are the equations of the asymptotes of a hyperbola
$\frac{x^2}{16}-\frac{y^2}{9}=1$

• A. $y=\frac{3}{4}x$
• B. $y=-\frac{4}{3}x$
• C. $y=\frac{4}{3}x$
• D. $y=-\frac{3}{4}x$

Answer 1

Answer: (A), (D)

$y=-\frac{3}{4}x$

Given: Hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$

To Find: Equations of asymptotes

We know that, the equation of the asymptotes of a hyperbola are given by
$y=\pm \frac{b}{a}x$.

From the given hyperbola equation, we have $a=4,b=3$

Substituting the $a\text{and}b$ value in the asymptote equation.
$y=\pm \frac{3}{4}x$

Hence, the asymptote equations are
$y=\frac{3}{4}x\text{and}y=-\frac{3}{4}x$.