find the equation of an ellipse from its graph?

Question

Can someone explain to me how to graph (x+2)²/9+(y-3)²/4=1 and other ellipses and how to find the equation of an ellipse from its graph?

Answer 1

Equation of ellipse .

The general equation of ellipse through the center is

In the given equation ,  .

So, ,  .

Every ellipse has symmetry with respect to two axis, one is major axis and another one is minor axis.

Length of major axis is 2b and length of minor axis is 2a.

The end points of these two axes can be determined as

End points on major axis

End points on minor axis

Now plot these points on the graph and draw the ellipse.

In this way you can find the graphs of other ellipses.

 

Now you can also find the equation of an ellipse with its graph by finding its center,

length of major and minor axis.

Let us take the graph of above given equation

From the graph

The center of the ellipse is .

The length of major axis is , therefore .

The length of minor axis is , therefore .

So, the equation of the ellipse is .