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Hyperbola center (0,0), focus (0,4), vertex (0, -2)

a) y² - x² = 4
b) x² - y² = 4
c) x² - y² = -4
d) y² - x² = -4

User Dylan B
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1 Answer

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The correct hyperbola equation with center (0,0), focus (0,4), and vertex (0, -2) is y² - x² = 4, which is option (a).

The student has provided the center, focus, and vertex of a hyperbola and asks which equation represents this hyperbola. The correct equation must account for the center being at the origin (0,0), the focus along the y-axis at (0,4), and the vertex on the y-axis at (0, -2). Considering the information, we know that the hyperbola is vertical (opens up and down) since the focus and vertex values are on the y-axis.

Therefore, the correct form of the hyperbola's equation is y² - x² = 4, represented by option (a), which corresponds to the standard form of a hyperbola equation Ay² - Bx² = C, where A and B are positive and the hyperbola opens along the y-axis.

User Colin Bernet
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