Chapter EP, Problem 10.6.11EP

To determine

To write: The equation in standard form, state the graph of the equation is a parabola, circle, ellipse, or hyperbola and then graph the equation.

Answer to Problem 10.6.11EP

The standard form of equation is $\frac{x^2}{49}+\frac{y^2}{9}=1$ , the equation is Ellipse and graph is shown in figure (1).

Explanation of Solution

Given:

The equation is $9x^2+49y^2=441$ .

Calculation:

Divide the above equation by 441.

$\begin{array}{c}\frac{9x^2}{441}+\frac{49y^2}{441}=\frac{441}{441}\\ \frac{x^2}{49}+\frac{y^2}{9}=1\end{array}$

The general form of Ellipse equation is $\frac{{\left(x-h\right)}^2}{a^2}+\frac{{\left(y-k\right)}^2}{b^2}=1$ .

Therefore, the given equation is Ellipse.

The graph of the equation $9x^2+49y^2=441$ or $\frac{x^2}{49}+\frac{y^2}{9}=1$ is as follows.

Figure (1)

Therefore, the standard form of equation is $\frac{x^2}{49}+\frac{y^2}{9}=1$ , the equation is Ellipse and graph is shown in figure (1).