Question 589278
y² = 36 + 4x².
<pre>
We have to get it in either the form:

{{{x^2/a^2}}} - {{{y^2/b^2}}} = 1

which looks like this  <font color="red">) (</font>
and has slopes of asymptotes {{{"" +- b/a}}}

or the form:

{{{y^2/a^2}}} - {{{x^2/b^2}}} = 1

which looks like this {{{drawing(40,40,8,12,8,12,
graph(40,40,8,12,8,12,10+sqrt(1+3(x-10)^2)),
graph(40,40,8,12,8,12,10-sqrt(1+3(x-10)^2)))}}}

and has slopes of asymptotes {{{"" +- a/b}}}

      y² = 36 + 4x²

y² - 4x² = 36

Get 1 on the right by dividing through by 36

{{{y^2/36}}} + {{{4x^2/36}}} = {{{36/36}}}

{{{y^2/36}}} + {{{x^2/9}}} = 1

{{{y^2/6^2}}} + {{{x^2/3^2}}} = 1


So, it's in the form

{{{y^2/a^2}}} - {{{x^2/b^2}}} = 1, with a=6, and b=3

which looks like this {{{drawing(40,40,8,12,8,12,
graph(40,40,8,12,8,12,10+sqrt(1+3(x-10)^2)),
graph(40,40,8,12,8,12,10-sqrt(1+3(x-10)^2)))}}}

and has slopes of asymptotes {{{"" +- a/b}}} = {{{"" +- 6/3}}} = ±2

Edwin</pre>