A curve $C$ has parametric equations $x = \sqrt{t}$, $y = t^2 + 4$, where \(0 \le t \le 1

Question

A curve $C$ has parametric equations $x = \sqrt{t}$, $y = t^2 + 4$, where $0 \le t \le 16$. Find the equation of the tangent to $C$ at the point $P$ with parameter $p$.[3] Given that the tangent in part (i) passes through the point $(0, 1)$, find the exact coordinate of the point $P$.[3] Sketch the curve $C$.[2]

Accepted Answer

(i) $y=4p^{\frac32}x-3p^2+4$. (ii) $P=(1,5)$. (iii) $y=x^4+4$, $0\le x\le4$, endpoints $(0,4)$ and $(4,260)$.

2025 MI P2 Q2

2025 MI P2 Q2

Solution:

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