Answer:
y^2/ 25 - x^2 / 9 = 1
Explanation:
Th standard form of a hyperbola is
[tex]\frac{(y-h)^2}{a^2}-\frac{(x-k)^2}{b^2}=1[/tex]
where (h,k ) are the coordinates of the centre and a and b are two constants.
The coordinates of the vertices are
[tex](h,k\pm a)[/tex]
and the equation of the asymptote is
[tex]y-\frac{a}{b}(x-h)+k[/tex]
Now, the coordinates of the center for our hyperbola are (0,0); therefore,
[tex](h,k)=(0,0)[/tex]
and the coordinates of the vertices we get from the graph are
[tex](h,k\pm a)=(0,\pm5)[/tex][tex]\therefore a=5[/tex]
Finally, the equation for the asymptote we get from the graph is
[tex]y=\frac{5}{3}x[/tex]
meaning
[tex]b=3[/tex]
Hence,
h = 0,
b = 0,
a = 5,
b = 3
thereofore, the equation of the hyperbola is
[tex]\frac{(y-0)^2}{5^2}-\frac{(x-0)^2}{3^2}=1[/tex][tex]\frac{y^2}{25}-\frac{x^2}{9}^{}=1[/tex]
which is our answer!
