Answer:
[tex]\frac{(y^2}{25}-\frac{x^2}{64}=1[/tex]
Step-by-step explanation:
We have been given an image of a hyperbola. We are asked to write an equation for our given hyperbola.
We can see that our given hyperbola is a vertical hyperbola as it opens upwards and downwards.
We know that equation of a vertical hyperbola is in form [tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex], where, [tex](h,k)[/tex] represents center of hyperbola.
'a' is vertex of hyperbola and 'b' is co-vertex.
We can see that center of parabola is at origin (0,0).
We can see that vertex of parabola is at point [tex](0,5)\text{ and }(0,-5)[/tex], so value of a is 5.
We can see that co-vertex of parabola is at point [tex](8,0)\text{ and }(-8,0)[/tex], so value of b is 8.
[tex]\frac{(y-0)^2}{5^2}-\frac{(x-0)^2}{8^2}=1[/tex]
Therefore, our required equation would be [tex]\frac{(y^2}{25}-\frac{x^2}{64}=1[/tex].
