SOLUTION: find equation of hyperbola where foci is (9,0) and hyperbola passes through (12,3)

Question 928231: find equation of hyperbola where foci is (9,0) and hyperbola passes through (12,3)
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
find equation of hyperbola where foci is (,) and hyperbola passes through (,)

The general formula of a hyperbola is:

Since, (, ) is a point on the hyperbola, we have:

........eq.(1)

Since the foci is (,), we have:

.....eq.(2)

Substituting (2) into (1), we have:

....common denominator is

....write as

solutions:
=>=>
=>=>

Suppose , from (2), we have:

=>rejected, since a square cannot be negative

Suppose , from (2), we have:
=> this solution is accepted

Thus, we have:

foci is (,) and (,)
hyperbola passes through (,)

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