Question 1204698
<br>
The slopes of the asymptotes being 4 and -4 does not mean a=4 and b=1.  It only means a/b=4.<br>
The given graph shows the larger y value when x=-2 has to be 1.  Use that to find a and then b:<br>
----------------------------------------------<br>
(revised presentation, after question from student....)
{{{(y+1)^2/a^2-(x+2)^2/b^2=1}}}<br>
When x = -2, the y value is 1:<br>
{{{(1+1)^2/a^2-(-2+2)^2/b^2=1}}}
{{{(2)^2/a^2-(0)^2/b^2=1}}}
{{{4/a^2=1}}}
{{{a^2=4}}}
{{{a=2}}}<br>
Then a/b=4 leads to b=1/2.<br>
That gives you the correct equation.<br>