Question

PLEASE HELP!!!

Answer 1

If you plot these points on a coordinate plane, you see that both vertices and foci lie on the y axis.  This means that you have a vertical hyperbola, and the equation looks like this: $\frac{(y-k) ^{2} }{ a^{2} } - \frac{(x-h) ^{2} }{ b^{2} } =1$ where h and k are the center.  When you look at your graph, the origin is dead center between the vertices.  (0, 0) is our h and k.  Now we need a, b, and c.  a is the distance between the center and the vertices, so our a = 4, and c is the distance between the center and the foci, so our c = 5.  Use these in Pythagorean's Theorem to solve for b: $(4) ^{2}+ b^{2}=(5) ^{2}$ and $16+ b^{2} =25$ and b = 3.  So we have all we need to do is replace all the variables.  Our equation then would be this one: $\frac{(y-0) ^{2} }{16} - \frac{(x-0) ^{2} }{9} =1$ or, simplified, $\frac{ y^{2} }{16} - \frac{ x^{2} }{9} =1$