The equation of a curve is $y = a\sqrt{2x+1} + b$, where $a$ and $b$ are constants. The e

Question

The equation of a curve is $y = a\sqrt{2x+1} + b$, where $a$ and $b$ are constants. The equation of the normal to the curve at the point $A$ where $x=4$ is $2y+3x=20$. Find the values of $a$ and of $b$. Given that the tangent and the normal to the curve at $A$ intersects the $x$-axis at $B$ and $C$, respectively, find the area of triangle $ABC$.

Accepted Answer

(i) $a=2,\ b=-2$ (ii) $\dfrac{52}{3}\text{ units}^2$

Differentiation - Tangents and Normals at a Point

Differentiation - Tangents and Normals at a Point

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