Describe the ellipse which is the graph of the equation $\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y + 6 ) ^ { 2 } } { 4 } =1$ .
A) center: $( 1 , - 6 )$ ; vertices: $( - 2 , - 6 )$ , $( 4 , - 6 )$
B) center: $( - 1,6 )$ ; vertices: $( - 3,6 )$ , $( 2,6 )$
C) center: $( 1 , - 6 )$ ; vertices: $( 3,0 )$ , $( - 3,0 )$
D) center: $( 1 , - 6 )$ ; vertices: $( 0,2 )$ , $( 0 , - 2 )$

Question

Quizplus · Accepted Answer

The center of the ellipse is given by the point $(h, k)$ in the general equation $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$, which is $(1, -6)$ for this equation. The vertices along the x-axis are found by adding and subtracting the square root of the denominator under the $x$ term ($\sqrt{9} = 3$) from the x-coordinate of the center, resulting in vertices at $(1-3, -6) = (-2, -6)$ and $(1+3, -6) = (4, -6)$.

Describe the Ellipse Which Is the Graph of the Equation (x−1)29+(y+6)24=1\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y + 6 ) ^ { 2 } } { 4 } =19(x−1)2​+4(y+6)2​=1

Describe the Ellipse Which Is the Graph of the Equation $\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y + 6 ) ^ { 2 } } { 4 } =1$