Choose the equation that matches the graph.
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A) $16 x ^ { 2 } - 9 y ^ { 2 } = 144$
B) $9 x ^ { 2 } + 16 y ^ { 2 } = 144$
C) $9 x ^ { 2 } - 16 y ^ { 2 } = 144$
D) $16 x ^ { 2 } + 9 y ^ { 2 } = 144$

Question

Choose the equation that matches the graph.
-
A) $16 x ^ { 2 } - 9 y ^ { 2 } = 144$ 
B) $9 x ^ { 2 } + 16 y ^ { 2 } = 144$ 
C) $9 x ^ { 2 } - 16 y ^ { 2 } = 144$ 
D) $16 x ^ { 2 } + 9 y ^ { 2 } = 144$

Quizplus · Accepted Answer

The graph is an ellipse with horizontal major axis and vertical minor axis. The formula for such an ellipse is $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ where (h,k) is the center of the ellipse, a is the distance from the center to the vertices along the major axis, and b is the distance from the center to the co-vertices along the minor axis. Comparing the equation in each choice with this formula, we can see that only choice D has the correct signs and values for a and b to match the graph. Specifically, in choice D, a = 2√2 and b = 2√3, which match the lengths of the major and minor axes of the ellipse in the graph.

Choose the Equation That Matches the Graph 16x2−9y2=14416 x ^ { 2 } - 9 y ^ { 2 } = 14416x2−9y2=144

Choose the Equation That Matches the Graph $16 x ^ { 2 } - 9 y ^ { 2 } = 144$