Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.
Vertical major axis passes through the points $( 0,7 ) \text { and } ( 5,0 )$ .

A) $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 5 } = 1$
B) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 49 } = 1$
C) $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 25 } = 1$
D) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } = 1$
E) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$

Question

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. 
Vertical major axis passes through the points $( 0,7 ) \text { and } ( 5,0 )$ .

A) $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 5 } = 1$
B) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 49 } = 1$
C) $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 25 } = 1$
D) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } = 1$
E) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$

Quizplus · Accepted Answer

The standard form of an ellipse with a vertical major axis and center at the origin is $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$, where $2a$ is the length of the major axis and $2b$ is the length of the minor axis. The point (0,7) indicates that the semi-major axis $a = 7$, so $a^2 = 49$. The point (5,0) indicates that the semi-minor axis $b = 5$, so $b^2 = 25$. Therefore, the correct equation is $\frac{x^2}{25} + \frac{y^2}{49} = 1$.

Find the Standard Form of the Equation of the Ellipse (0,7) and (5,0)( 0,7 ) \text { and } ( 5,0 )(0,7) and (5,0)

Find the Standard Form of the Equation of the Ellipse $( 0,7 ) \text { and } ( 5,0 )$