Chapter 9.3, Problem 104E

To determine

To find: The similarities and differences between the hyperbolas $\frac{x^2}{16}-\frac{y^2}{9}=1$ and $\frac{y^2}{9}-\frac{x^2}{16}=1$ and verify the answer with the help of graph.

Answer to Problem 104E

The hyperbolas $\frac{x^2}{16}-\frac{y^2}{9}=1$ and $\frac{y^2}{9}-\frac{x^2}{16}=1$ have the center origin, but the difference in both the hyperbolas is the focus of first hyperbola lies on $x$ -axis and focus of second hyperbola lies on $y$ -axis.

Explanation of Solution

Given information:

The equation of hyperbolas are $\frac{x^2}{16}-\frac{y^2}{9}=1$ and $\frac{y^2}{9}-\frac{x^2}{16}=1$ .

Calculation:

Both the hyperbolas $\frac{x^2}{16}-\frac{y^2}{9}=1$ and $\frac{y^2}{9}-\frac{x^2}{16}=1$ have center at origin.

The difference between both the hyperbolas is the focus of first hyperbola lies on $x$ -axis and the focus of second hyperbola lies on $y$ -axis.

Check the graph of both the hyperbolas.

  

Figure(1)