Answer
See graph
Work Step by Step
We are given the hyperbola:
$\dfrac{(x+2)^2}{9}-\dfrac{(y-1)^2}{25}=1$
The equation is in the standard form:
$\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1$
The transverse axis is parallel to the $x$-axis.
Determine $h,k,a,b,c$:
$h=-2$
$k=1$
$a^2=9\Rightarrow a=\sqrt 9=3$
$b^2=25\Rightarrow b=\sqrt {25}=5$
$c^2=a^2+b^2$
$c^2=9+25$
$c^2=34$
$c=\sqrt{34}$
Determine the centre of the hyperbola:
$(h,k)=(-2,1)$
Determine the coordinates of the vertices:
$(h-a,k)=(-2-3,1)=(-5,1)$
$(h+a,k)=(-2+3,1)=(1,1)$
Determine the coordinates of the foci:
$(h-c,k)=(-2-\sqrt{34},1)$
$(h+c,k)=(-2+\sqrt{34},1)$
Determine the asymptotes:
$y-k=\pm\dfrac{b}{a}(x-h)$
$y-1=\pm\dfrac{5}{3}(x+2)$
Graph the hyperbola:
