Identify the type of ellipse. Horizontal ellipses fit the equation (x-h)^2a^2+ (y-k)^2b^2=1, and vertical ellipses fit the equation (x-h)^2b^2+ (y-k)^2a^2=1. In both cases, a and b are positive numbers such that a>b.
B
Practice makes perfect
We want to identify the y-coordinate of the center of the ellipse. To do so, we will rewrite the given equation just a little bit.
Notice that the denominator of the expression containing the y-variable is greater than the denominator of the expression that contains the x-variable. Therefore, we have a vertical ellipse. Let's recall the main characteristics of this type of ellipse.
Vertical Ellipse
Standard-Form Equation
(x- h)^2/b^2+(y- k)^2/a^2=1
Center
( h, k)
Vertices
( h, k± a)
Co-vertices
( h ± b, k)
Foci
( h, k± c)
a,b,c relationship, a>b>0
c^2= a^2- b^2
Let's consider our equation one more time.
(x-( - 9))^2/2^2+(y-( - 4))^2/3^2=1
We can see that a= 3, b= 2, h= - 9, and k= - 4. Now, we will substitute h= - 9, and k= - 4 into the formula for the center.
( h, k) ⇒ ( - 9, - 4)
The y-coordinate of the center is equal to - 4. This corresponds to option B.
