Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 16x² – 9y² = 576

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Solution

The given equation is 16x² – 9y² = 576.

It can be written as

16x² – 9y² = 576

On comparing equation (1) with the standard equation of hyperbola i.e.,, we obtain a = 6 and b = 8.

We know that a² + b² = c².

Therefore,

The coordinates of the foci are (±10, 0).

The coordinates of the vertices are (±6, 0).

Length of latus rectum

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