Choose the equation that matches the graph.
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A) $4 x ^ { 2 } - 25 y ^ { 2 } = 100$
B) $4 y ^ { 2 } - 25 x ^ { 2 } = 100$
C) $25 x ^ { 2 } + 4 y ^ { 2 } = 100$
D) $25 x ^ { 2 } - 4 y ^ { 2 } = 100$

Question

Choose the equation that matches the graph.
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A) $4 x ^ { 2 } - 25 y ^ { 2 } = 100$ 
B) $4 y ^ { 2 } - 25 x ^ { 2 } = 100$ 
C) $25 x ^ { 2 } + 4 y ^ { 2 } = 100$ 
D) $25 x ^ { 2 } - 4 y ^ { 2 } = 100$

Quizplus · Accepted Answer

The graph represents a hyperbola, and the standard form equation for a hyperbola with the major axis parallel to the x-axis is given by $\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$, where $(h,k)$ is the center of the hyperbola, $a$ is the distance from the center to each vertex along the major axis, and $b$ is the distance from the center to each vertex along the minor axis.

In this case, the center of the hyperbola is at the origin (0,0) and the vertices are located at (0,-5) and (0,5), indicating that $a=5$. Along the minor axis, the distance between the two foci is given by $\sqrt{b^2 + c^2} = 2$, where $c$ is the distance from the center to each focus. Since $c^2 = a^2 + b^2$, we have $b^2 + a^2 = c^2 = 4^2 = 16$, which means $b=3$.

Plugging in these values, we get the equation $25x^2 - 4y^2 = 100$, which is equivalent to choice D.

Choose the Equation That Matches the Graph 4x2−25y2=1004 x ^ { 2 } - 25 y ^ { 2 } = 1004x2−25y2=100

Choose the Equation That Matches the Graph $4 x ^ { 2 } - 25 y ^ { 2 } = 100$