Answer:
The equation in standard form is y^2/4 - x^2/45 = 1
Step-by-step explanation:
As vertices at (0, ±2), the hyperbola opens up and down,
the standard form for a hyperbola that opens up and down is:
(y - k)^2 / a^2 - (x - h)^2 / b^2 = 1,
where its center is located at (h, k);
a is 2x distance between the vertices;
c is 2x distance between the foci;
and b^2 = c^2 - a^2
As vertices are at (0, ±2) and foci are at (0, ±7),
a=2 and c=7
a^2 = 2^2 = 4
b^2 = c^2 - a^2
= 7^2 - 2^2
= 45
The center is at the mid-pt between vertices,
so it is at (0, 0)
h=0 and k=0
Substituting a^2, b^2, h and k in the standard form,
y^2/4 - x^2/45 = 1
