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Triangle in Parabola

Algebra Level 2

There are three points \(A=(1, 0),\) \(B=(4, 3)\) and \(C=(a, b)\) on the parabola \(y=-x^2+6x-5.\) What is the maximum area of the triangle \(ABC?\)

\[\frac{29}{8}\] \[\frac{27}{8}\] \[\frac{7}{2}\] \[\frac{15}{4}\]

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by Kumar Gupta

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