Question

The asymptotes of the hyperbola $36y^2-25x^2+900=0$, are:

• A. $y=\pm \frac{6}{5}x$
• B. $y=\pm \frac{5}{6}x$
• C. $y=\pm \frac{36}{25}x$
• D. $y=\pm \frac{25}{36}x$

Answer 1

Answer: (B)

$y=\pm \frac{5}{6}x$

Given hyperbola is $36y^2-25x^2+900=0$

$\Rightarrow 36y^2-25x^2=-900$

$\Rightarrow 25x^2-36y^2=900$

Divide by $900$ on both sides we get

$\frac{x^2}{36}-\frac{y^2}{25}=1$ which is a standard form of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$.

Therefore $a^2=36,b^2=25$

$\Rightarrow a=6,b=5$

The equations of the asymptotes are given by $y=\pm \frac{b}{a}x$

$\Rightarrow y=\pm \frac{5}{6}x$