Question

Which equations represent the asymptotes of the hyperbola (x-1)^2/36-(y-2)^2/64=1 ?

Answer 1

Using the equation given, it is found that the asymptotes of the hyperbola are given by:

• $y = 2 \pm \frac{4}{3}(x - 1)$

What is the equation of a hyperbola?

The equation of an hyperbola with horizontal transverse axis and center at $(x_0, y_0)$ is given by:

$\frac{(x - x_0)^2}{a^2} + \frac{(y - y_0)^2}{b^2} = 1$

The asymptotes are given by:

$y = y_0 \pm \frac{b}{a}(x - x_0)$

In this problem, the equation is:

$\frac{(x - 1)^2}{36} + \frac{(y - 2)^2}{64} = 1$

Hence the coefficients are:

$x_0 = 1, y_0 = 2, a = 6, b = 8$

Then, the equation of the asymptotes is:

$y = y_0 \pm \frac{b}{a}(x - x_0)$

$y = 2 \pm \frac{8}{6}(x - 1)$

$y = 2 \pm \frac{4}{3}(x - 1)$

You can learn more about hyperbolas at https://brainly.com/question/20776156