Question

Write an equation in standard form for the hyperbola

Answer 1

graph as well as the answer choices

Answer 2

The answer is a. Here's how. I'll do my best with the explanation in this forum. Because the hyperbola lie on the y axis, the vertices and the foci are on the y axis, and also the y^2 term comes first. The standard form for this hyperbola is\[\frac{ y ^{2} }{ a ^{2} }-\frac{ x ^{2} }{ b ^{2} }=1\]Because it is centered at the origin, it is just y^2 and x^2 in both the numerators. The a^2 term is the square of how many units it is from the center to the vertice. From the center to the vertice is 10 units, so 10^2 is the denominator under the y term. Now let's do the same with the x term. From the center to where the asymptotes form a square is 8 units. Don't forget that the units on your graph are going up by2 units, not 1. 8^2 is 64, so 64 is the number that goes under your x term. And there you go!