Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola

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Solution

The given equation is.

On comparing this equation with the standard equation of hyperbola i.e.,, we obtain a = 3 and.

We know that a² + b² = c².

Therefore,

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

The coordinates of the vertices are (0, ±3).

Length of latus rectum

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Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola

The given equation is. On comparing this equation with the standard equation of hyperbola i.e.,, we obtain a = 3 and. We know that a2 + b2 = c2. Therefore, The coordinates of the foci are (0, ±6). The coordinates of the vertices are (0, ±3). Length of latus rectum

The given equation is.

On comparing this equation with the standard equation of hyperbola i.e.,, we obtain a = 3 and.

We know that a² + b² = c².

Therefore,

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

The coordinates of the vertices are (0, ±3).

Length of latus rectum