The curve $C$ is defined parametrically by $x={{t}^{2}}$ and $y={{t}^{3}}$. Find the equation

Question

The curve $C$ is defined parametrically by $x={{t}^{2}}$ and $y={{t}^{3}}$. Find the equation of the tangent to the curve at the point $(16,\ 64)$, and the coordinates of the point at which this tangent meets the curve again.[4] A rectangular piece of paper is $24$ cm long and $12$ cm wide. The upper right-hand corner is folded down to reach the bottom edge of the paper at $C$ as shown below. Show that $\vartriangle APC$ and $\vartriangle CQB$ are similar triangles and hence show that $x=\frac{\sqrt{6y}}{\sqrt{y-6}}$.[4] By using differentiation, find the minimum length of the resulting crease $AB$.[5]

Accepted Answer

(a) $(4, -8)$ (b) min $AB = 15.6$ cm

2018 AJC Promo Q9

2018 AJC Promo Q9

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