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.
Finding the Key Features
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- 0)^2/4^2+(y- )^2/3^2=1
We see that a= 4, b= 3, h= 0, and k= . The only value we do not know is c. Let's find it!
