Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas: (i) x2/9 – y2/16 = 1, (ii) y2 – 16x2 = 16

Question

CASE_STUDIESStandard Equation of HyperbolaEccentricity of HyperbolaLatus Rectum of Hyperbola2 sub-questions

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Find the equation of the hyperbola with foci (0, ± 3) and vertices (0, ± √11/2).

Find the equation of the hyperbola where foci are (0, ±12) and the length of the latus rectum is 36.

Latus Rectum of Hyperbola

y2/9 – x2/27 = 1

9y2 – 4x2 = 36

16x2 – 9y2 = 576

5y2 – 9x2 = 36