Write an equation for the ellipse.
-foci at $( 1,7 ) , ( 1,1 )$; major axis length of 10
A) $\frac { ( y - 4 ) ^ { 2 } } { 25 } + \frac { ( x - 1 ) ^ { 2 } } { 16 } = 1$

B) $\frac { ( y - 4 ) ^ { 2 } } { 25 } + \frac { ( x + 1 ) ^ { 2 } } { 16 } = 1$

C) $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 25 } = 1$

D) $\frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$

Question

Write an equation for the ellipse.
-foci at $( 1,7 ) , ( 1,1 )$; major axis length of 10
A) $\frac { ( y - 4 ) ^ { 2 } } { 25 } + \frac { ( x - 1 ) ^ { 2 } } { 16 } = 1$

B) $\frac { ( y - 4 ) ^ { 2 } } { 25 } + \frac { ( x + 1 ) ^ { 2 } } { 16 } = 1$

C) $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 25 } = 1$

D) $\frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$

Quizplus · Accepted Answer

The foci are vertically aligned (same x-coordinate), indicating the major axis is vertical. The center is midway between the foci at $(1, 4)$. The major axis length of 10 implies a semi-major axis ($a$) of 5, so $a^2 = 25$. The distance between the center and either focus (c) is 3, so $b^2 = a^2 - c^2 = 25 - 9 = 16$. The equation is $\frac{(y - 4)^2}{25} + \frac{(x - 1)^2}{16} = 1$.

Write an Equation for the Ellipse (1,7),(1,1)( 1,7 ) , ( 1,1 )(1,7),(1,1)

Write an Equation for the Ellipse $( 1,7 ) , ( 1,1 )$