Question

Prove Theorem 9.20 (b). That is, show that the graph of the equation satisfies$\frac{y^2}{B^2}-\frac{x^2}{A^2}=1$ Definition 9.19, where the points with coordinates $\left(0,\pm \sqrt{A^2+B^2}\right)$ are the foci of the hyperbola

Short answer

Hence, proved

Step-by-step solution

Given information

The given equation of a parabola is$\frac{y^2}{B^2}-\frac{x^2}{A^2}=1$

Stp 2: Graph the parabola and find the vertices and foci.

The graph of the parabola $\frac{y^2}{B^2}-\frac{x^2}{A^2}=1$is ,

The coordinates of the hyperbola are$\left(0,\pm \sqrt{A^2+B^2}\right)$

As, from the graph it is clear that the points with coordinates $\left(0,\pm \sqrt{A^2+B^2}\right)$

are the foci of the hyperbola.