Answer
The graph is an ellipse with center at $(0,0)$, major axis at $(0,4)$ and $(0,-4)$, and minor axis at $(-3,0)$ and $(3,0)$.
Work Step by Step
The graph of an equation of the form $$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} =1$$ is an ellipse with center at point $(0,0)$.
The x-intercepts are at points $(a,0)$ and $(-a,0)$ and the y-intercepts are at points $(0,b)$ and $(0,-b)$.
Hence, the equation $$16x^2 + 9y^2 = 144$$ should be rewritten to conform to the format as above. Dividing both sides by $144$ will yield to: $$\frac{x^{2}}{9}-\frac{y^{2}}{16} =1$$
Since the larger number is under the $y$, then the graph will be a vertical ellipse. So, $$a = \sqrt 9$$ $$a= 3$$ and $$b = \sqrt {16}$$ $$b= 4$$
We can now use $a$ and $b$ to plot the ends of the major and minor axis. This parabola is vertical and the value of $a (3)$ is the distance from the center point $(0,0)$ to the end of the minor axis.
On the other hand, the value of $b (4)$ will be the distance from the center to the end of the major axis. The resulting graph will then be:
