We can see that the binomials containing the variables are both raised to the power of 2 and are both positive. Moreover, the denominator of the binomial containing the x-variable is greater than the denominator of the binomial that contains the y-variable. Therefore, our equation matches the format of a horizontalellipse.
Graphing the Ellipse
Let's recall the main characteristics of this type of ellipse.
Horizontal Ellipse
Standard-Form Equation
(x- h)^2/a^2+(y- k)^2/b^2=1
Center
( h, k)
Vertices
( h± a, k)
Co-vertices
( h, k± b)
Foci
( h± c, k)
a,b,c relationship, a>b>0
c^2= a^2- b^2
Consider our equation one more time.
(x- 3)^2/6^2+(y-( - 2))^2/3^2=1
We see that a= 6, b= 3, h= 3, and k= - 2. The only value we do not know is c. Let's find it!
Note that we only took the principal root, because to find the foci we will add and subtract the value of c. Therefore, its sign is irrelevant. We can now write the desired information.
