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Question

Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas. 9y24x2=36

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Solution

Given hyperbola:9y24x2=36
Dividing it whole by 36 , y24x29=1
where b=2,a=3
Its a conjugate hyperbola so it will have different formula than the normal hyperbola.
Eccentricity e=1+a2b2=1+94=1213
Vertices, A (0,±b)(0,±2)
Foci(0,±be)(0,±21213)(0,±13)
Length of LR =2a2b=294=92 unit length.


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