The points $A$ and $B$ lie on the curve $y=8+2x-x^2$, where the $x$-coordinates of $A$ and

Question

The points $A$ and $B$ lie on the curve $y=8+2x-x^2$, where the $x$-coordinates of $A$ and $B$ are $-1$ and $3$, respectively. Find the equation of the chord $AB$.[2] Hence find the area enclosed by the curve and the chord.[4]

Accepted Answer

(i) $y=5$ (ii) $\dfrac{32}{3}\text{ units}^2$

Area between a parabola and a chord

Area between a parabola and a chord

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