Answer
Refer to the graph below.
Work Step by Step
The given equation is equivalent to:
$\dfrac{(x-4)^2}{4^2} + \dfrac{(y-3)^2}{3^2}=1$
RECALL:
The graph of the equation $\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2}=1$ where $a \gt b$ is a horizontal ellipse whose center is at $(h, k)$ and whose major axis is $2a$ units long and whose minor axis is $2b$ units long.
The equation above is in the same form as the one in the recall part above with $h=4, k=3, a=4,$ and $b=3$.
Thus, its graph is a horizontal ellipse whose center is at $(4, 3)$ and whose major axis is $8$ units long and whose minor axis is $6$ units long.
To graph the ellipse, perform the following steps:
(1) Plot the following points:
center: $(4, 3)$
vertices: $(4-4, 3)=(0, 3)$ and $(4+4, 3)=(8, 3)$ (endpoints of the major axis)
endpoints of the minor axis: $(4, 3-3) = (4, 0)$ and $(4, 3+3)=(4. 6)$
(2) Connect the points (excluding the center) using a smooth curve to form an ellipse.
Refer to the graph above.
