Choose the equation that matches the graph.
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A) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$
B) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 9 } = 1$
C) $\frac { y ^ { 2 } } { 5 } + \frac { x ^ { 2 } } { 3 } = 1$
D) $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 9 } = 1$

Question

Choose the equation that matches the graph.
-
A) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$ 
B) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 9 } = 1$ 
C) $\frac { y ^ { 2 } } { 5 } + \frac { x ^ { 2 } } { 3 } = 1$ 
D) $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 9 } = 1$

Quizplus · Accepted Answer

The graph is an ellipse with the center at the origin and horizontal and vertical axis lengths of 6 and 10, respectively. The equation of an ellipse with center at the origin and horizontal and vertical axis lengths of a and b, respectively, is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. Substituting the given axis lengths into this equation, we get $\frac{x^2}{9}+\frac{y^2}{25}=1$, which is equivalent to answer choice D.

Choose the Equation That Matches the Graph x225+y29=1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 125x2​+9y2​=1

Choose the Equation That Matches the Graph $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$