What is the standard equation of a horizontal hyperbola with center at origin and a = 5, b = 3?

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Multiple Choice

What is the standard equation of a horizontal hyperbola with center at origin and a = 5, b = 3?

Explanation:
A horizontal hyperbola centered at the origin uses the form x^2/a^2 − y^2/b^2 = 1. Since the center is at (0,0) there are no shifts, and with a = 5 and b = 3 we get a^2 = 25 and b^2 = 9. Plugging those in gives x^2/25 − y^2/9 = 1. The minus sign between the terms tells you it’s a hyperbola (not an ellipse, which would use a plus). Because the x-term is the positive one, the transverse axis runs along the x-axis, so the hyperbola opens left and right. The asymptotes would be y = ±(b/a)x = ±(3/5)x, which aligns with this orientation.

A horizontal hyperbola centered at the origin uses the form x^2/a^2 − y^2/b^2 = 1. Since the center is at (0,0) there are no shifts, and with a = 5 and b = 3 we get a^2 = 25 and b^2 = 9. Plugging those in gives x^2/25 − y^2/9 = 1. The minus sign between the terms tells you it’s a hyperbola (not an ellipse, which would use a plus). Because the x-term is the positive one, the transverse axis runs along the x-axis, so the hyperbola opens left and right. The asymptotes would be y = ±(b/a)x = ±(3/5)x, which aligns with this orientation.

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