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Question

If the distance between the foci of a hyperbola is 16 and its ecentricity is 2, then obtain its equation.

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Solution

We have
2ae=16ae=8a=82=42a2=32
Now,
ae2=a2+b282=32+b264-32=b2b2=32


Therefore, the equation of the hyperbola is given by
x232-y232=1x2-y2=32

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