Question

Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7)

Answer 1

so, I gather you know the equation of a hyperbola?

Answer 2

well @n14r96
the vertices are at (0, +3) and (0, -3)
the "x" doesn't change
the "y" does
meaning is going upwards, thus is a vertical traversal axis

Answer 3

the distance from one vertex to the other is 3+3, so 6
half-way through is the (h,k) center

the distance for the "a" element in the formula is the distance from the center to the vertex
so the vertices are at (0, +3) and (0, -3), so the "a" distance is 3
so a = 3

the foci are at (0, ±7)

the distance from the center to a focus is "c"
you center is at (0,0) your foci at (0, ±7)
so the "c" distance is 7
c = 7

so, what about "b"?

\(c^2=a^2+b^2 \implies 7^2 = 3^2+b^2\)

solve for \(b^2\)

the equation uses \(a^2 \ and \ b^2\)
so since a = 3, \(a^2 = 9\)

Answer 4

and of course, your center is at (0,0)

Answer 5

so y^2/49-x^2/9=1 ???