Find the standard form of the equation of the ellipse satisfying the given conditions.
-Endpoints of major axis: $( 1 , - 3 )$ and $( 1,7 )$; endpoints of minor axis: $( - 3,2 )$ and $( 5,2 )$;
A) $\frac { ( x - 1 ) ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 25 } = 1$
B) $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 1$
C) $\frac { ( x + 1 ) ^ { 2 } } { 16 } + \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$
D) $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$

Question

Quizplus · Accepted Answer

The center of the ellipse is the midpoint of both the major and minor axes, which is $(1, 2)$. The length of the major axis is 10 (from -3 to 7), so $a=5$ and $a^2=25$. The length of the minor axis is 8 (from -3 to 5), so $b=4$ and $b^2=16$. The standard form is $\frac{(x-1)^2}{16} + \frac{(y-2)^2}{25} = 1$.

Find the Standard Form of the Equation of the Ellipse (1,−3)( 1 , - 3 )(1,−3)

Find the Standard Form of the Equation of the Ellipse $( 1 , - 3 )$