A curve $C$ has parametric equations \[x = \sin^2 t, \quad y = 1 + 2 \sin t, \quad -\frac{\pi}{2}

Question

A curve $C$ has parametric equations $$x = \sin^2 t, \quad y = 1 + 2 \sin t, \quad -\frac{\pi}{2} \le t \le \frac{\pi}{2}$$ Sketch $C$, stating clearly the coordinates of the endpoints and the coordinates of the $y$-intercept(s).[2] Find the exact cartesian equation of $l$, the normal to $C$ at the point $\left(\frac{1}{4}, 2\right)$.[4]

Accepted Answer

(a) Included endpoints $(1,-1)$, $(1,3)$; y-intercept $(0,1)$. Diagram shown. (b) $y=-\frac12x+\frac{17}8$, or $8y=-4x+17$.

2025 CJC P1 Q3

2025 CJC P1 Q3

Solution:

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