Chapter 11.10, Problem 43PPSE

Solution

To find: To graph the equation, to identify the conic section and to describe the graph and its line of symmetry. Then to find the domain and range.

The conic is an ellipse with center at $\left(0,0\right)$ with major axis x axis and minor axis along y axis. The lines of symmetry are $x=0,y=0$ . The domain is $\left[-5,5\right]$ and range is $\left[-3,3\right]$ .

Given information:

Given,equation is $9x^2+25y^2=225$

Calculation:

Graphing the equation using a graphing calculator:

  

The conic is an ellipse with center at $\left(0,0\right)$ with major axis along the x -axis with ends at $\left(-5,0\right),\left(5,0\right)$ and the minor axis along y -axis with ends at $\left(0,-3\right),\left(0,3\right)$

For an ellipse centered at the origin with major axis along the x axis, the x and y axes are the lines of symmetry.

Hence,the lines of symmetry are $x=0,y=0$ .

From the figure, it is seen that xvalues lie between $\left[-5,5\right]$ and yvalues lie between $\left[-3,3\right]$ .

Hence the domain is $\left[-5,5\right]$ and range is $\left[-3,3\right]$ .

Conclusion:

Hence, the conic is an ellipse with center at $\left(0,0\right)$ with major axis x axis and minor axis along y axis. The lines of symmetry are $x=0,y=0$ . The domain is $\left[-5,5\right]$ and range is $\left[-3,3\right]$ .