1Cademy - Example: Graphing $$\frac{x^2}{25}

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How to Graph a Hyperbola with Center $(0, 0)$

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Example: Graphing $\frac{x^2}{25} - \frac{y^2}{4} = 1$

To graph the equation $\frac{x^2}{25} - \frac{y^2}{4} = 1$ , apply the six-step procedure for graphing a hyperbola centered at $(0, 0)$ . Step 1: The equation is already in standard form. Step 2: Because the $x^2$ -term is positive, the transverse axis is horizontal. Step 3: Since $a^2 = 25$ , then $a = \pm 5$ , so the vertices are at $(-5, 0)$ and $(5, 0)$ . Step 4: Since $b^2 = 4$ , then $b = \pm 2$ . Sketch the central rectangle intersecting the $x$ -axis at the vertices and the $y$ -axis at $(0, -2)$ and $(0, 2)$ . Step 5: Sketch the asymptotes through the diagonals of the rectangle; their equations are $y = \frac{2}{5}x$ and $y = -\frac{2}{5}x$ . Step 6: Draw the two branches of the hyperbola starting at each vertex, using the asymptotes as guides. The branches open to the left and right.

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Updated 2026-05-25

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OpenStax Intermediate Algebra

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