Chapter 9.5, Problem 15PPS

To determine

To Plot: The graph of given hyperbola

Explanation of Solution

Given:

  $\frac{y^2}{9}-\frac{x^2}{49}=1$

Formula Used:

  $\begin{array}{l}\frac{{\left(y-k\right)}^2}{a^2}-\frac{{\left(x-h\right)}^2}{b^2}=1\\ \frac{y^2}{a^2}-\frac{x^2}{b^2}=1\\ y=\frac{b}{a}xor=-\frac{b}{a}x\\ e=\frac{\sqrt{a^2+b^2}}{a}\\ l=\frac{2b^2}{a}\end{array}$

Calculation:

  

  $\begin{array}{l}a=3\\ b=7\\ \left(h,k\right)=\left(0,0\right)\\ p=\frac{b^2}{\sqrt{a^2+b^2}}=\frac{49}{\sqrt{49+9}}\\ =\frac{49}{\sqrt{58}}\\ \text{Asymptotes}\\ y=\pm \frac{7}{3}x\\ Vertices\\ \left(0,3\right)\&\left(0,-3\right)\end{array}$