An elliptical stained-glass insert is to be fitted in a 4ft by 6ft rectangular opening (see figure). Using the coordinate system shown,find an equation for the ellipse.
A) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$
B) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$
C) $$\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$$
D) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 4 } = 1$
E) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 6 } = 1$

Question

An elliptical stained-glass insert is to be fitted in a 4ft by 6ft rectangular opening (see figure).  Using the coordinate system shown,find an equation for the ellipse. ​
A) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ 
B) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$ 
C) $$\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$$ 
D) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 4 } = 1$ 
E) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 6 } = 1$

Quizplus · Accepted Answer

The given rectangular opening has dimensions of 4ft by 6ft. The center of the ellipse is at point (2,3) which is the midpoint of the given rectangular opening. The length of the major axis is 6ft, because it goes from the top to the bottom of the opening. The length of the minor axis is 4ft, because it goes from the left to the right of the opening. Thus, the equation of the ellipse is:

((x-2)/2)^2 + ((y-3)/3)^2 = 1

Expanding this formula and simplifying, we get option B as the correct answer.

An Elliptical Stained-Glass Insert Is to Be Fitted in a 4ft