Question

Can someone tell me what are the steps to solving this?

Answer 1

The general equation of an ellipse is

`((x-x_0)^2)/(a^2)+((y-y_0)^2)/(b^2) = 1`

where:

• 
  `x_0` is the x coordinate of the center
• 
  `y_0` is the y coordinate of the center
• 
  `a` is half the length of the major axis
• 
  `b` is half the length of the minor axis

So, in your case, we have
`(x_0,y_0)=(2,3)`, and the equation will look like this:

`((x-2)^2)/(a^2)+((y-3)^2)/(b^2) = 1`

Moreover, we know that the major axis is horizontal (i.e. it involves the x coordinate). Its length is 8, which implies
`a=4`

Similarly, the minor axis has length 4, which implies
`b=2`

So, the complete equation is

`((x-2)^2)/(16)+((y-3)^2)/(4) = 1`