Question 167394
The first equation is an ellipse. This is an example of a conic section.

The first step is to divide each term by 144. The equation now becomes x^2/9+y^2/16=1

Make y=0 so that you can determine where the x intercets are on the x axis

what 2 numbers squared make the equation =1? It would be + or -3. Make dots on the x axis at these two points on the axis. Then make x=0 what two values make the equation =1  + or -4. These are your y intercepts. Connect the together to form an oval. A circle is a special type of an ellipse.

The second equation is a hyperbola

x^2/9-(y+2)^2/9=1

Again make y=0

x= + or - 3. Plot these points.

the y has no value but they are the limits of the equation.

Draw two dashed lines at y= +3 and at y=-3 straight across the graph. Make a horseshoe graph at x=+3 and x=-3 but never touching the two dashed lines. This is the vertex of the graph at each side. Therefore you have two horseshoe graph going to infinity in opposite directions.