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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{27}{8}

\frac{15}{4}

\frac{29}{8}

\frac{7}{2}

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by Kumar Gupta

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