Write an equation for the ellipse.
-minor axis from $( - 3,3 )$ to $( 1,3 )$; major axis from $( - 1 , - 1 )$ to $( - 1,7 )$
A) $\frac { ( \mathrm { x } - 2 ) ^ { 2 } } { 4 } + \frac { ( \mathrm { y } - 4 ) ^ { 2 } } { 16 } = 1$

B) $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1$

C) $\frac { ( x - 3 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$

D) $\frac { ( x - 1 ) ^ { 2 } } { 4 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$

Question

Write an equation for the ellipse.
-minor axis from $( - 3,3 )$ to $( 1,3 )$; major axis from $( - 1 , - 1 )$ to $( - 1,7 )$
A) $\frac { ( \mathrm { x } - 2 ) ^ { 2 } } { 4 } + \frac { ( \mathrm { y } - 4 ) ^ { 2 } } { 16 } = 1$

B) $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1$

C) $\frac { ( x - 3 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$

D) $\frac { ( x - 1 ) ^ { 2 } } { 4 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$

Quizplus · Accepted Answer

The center of the ellipse is the midpoint of both the major and minor axes. For the minor axis from $(-3,3)$ to $(1,3)$, the midpoint is $(-1,3)$. For the major axis from $(-1,-1)$ to $(-1,7)$, the midpoint is also $(-1,3)$, confirming the center of the ellipse is $(-1,3)$. The length of the major axis is 8 (from -1 to 7), so the semi-major axis $a=4$, and the length of the minor axis is 4 (from -3 to 1), so the semi-minor axis $b=2$. Therefore, the equation of the ellipse in standard form is $\frac{(x+1)^2}{4} + \frac{(y-3)^2}{16} = 1$.

Write an Equation for the Ellipse (−3,3)( - 3,3 )(−3,3) To (1,3)( 1,3 )(1,3)

Write an Equation for the Ellipse $( - 3,3 )$ To $( 1,3 )$