Question

In Problems$11-18$, find an equation of the conic described. Graph the equation by hand.

Center at$(-1,2)$;$a=3;c=4$; transverse axis parallel to the$x-$axis.

Short answer

The equation of the hyperbola is$\frac{{(x+1)}^2}{9}-\frac{{(y-2)}^2}{7}=1$

Step-by-step solution

Step 1. Given Information

Centr at$(-1,2)$;$a=3\&c=4$, transverse axis parallel to$x-$axis.

Step 2. Calculation 

Since, $a=3\&c=4$

Then $c^2-a^2=16-9$

$=7$

and the transverse axis is parallel to $x-$axis

then equation is

$\frac{{(x+1)}^2}{9}-\frac{{(y-2)}^2}{7}=1$

Step 3. Graph