A curve $C$ has equation $y = \frac{a}{2bx - x^2}$, where $a, b 0$. Describe the tra

Question

A curve $C$ has equation $y = \frac{a}{2bx - x^2}$, where $a, b > 0$. Describe the transformation that maps the graph of $C$ onto the graph of $y = \frac{a}{b^2 - x^2}$.[2] Given that $a = 1$ and $b = 2$, sketch $C$ stating the equations of any asymptotes and coordinates of any stationary points and of the points where the curve crosses the axes.[2]

Accepted Answer

(a) Translation by vector $\begin{pmatrix}-b\0\end{pmatrix}$ (b) Asymptotes $x=0$, $x=4$ and $y=0$, minimum point $\left(2,\dfrac14\right)$, and no axis crossings

2025 TJC P1 Q3

2025 TJC P1 Q3

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