The curves $C_{1}$ and $C_{2}$ have equations $\frac{x^2}{9}-\frac{y^2}{4}=1$ and \(y^2+x^2=k^

Question

The curves $C_{1}$ and $C_{2}$ have equations $\frac{x^2}{9}-\frac{y^2}{4}=1$ and $y^2+x^2=k^2$ respectively, where $k$ is a positive constant. Sketch $C_{1}$ and $C_{2}$ on the same diagram, stating the coordinates of any points of intersection with the axes and the equations of any asymptotes.[3] State the range of values of $k$ for $C_{1}$ and $C_{2}$ to intersect.[1] State the equations of the common lines of symmetry for both $C_{1}$ and $C_{2}$.[1] The function $\mathrm{f}$, with domain the set of all real values, is given by$$\mathrm{f}(x)=\begin{cases}-2x+6 & \text{for}\hspace{0.5em} 0 < x \le 3, \ 3x-9 & \text{for}\hspace{0.5em} 3 < x \le 5, \end{cases}$$and that $\mathrm{f}(x)=\mathrm{f}(x+5)$. Find $\mathrm{f}(46)$.[1] Sketch the graph of $y=\mathrm{f}(x)$ for $-5 \le x \le 5$.[2] Hence, state the roots of $\mathrm{f}(-x)=0$ for $-5 \le x \le 5$.[1]

Accepted Answer

(a)(ii) $k\geq3$ (a)(iii) $x=0$ and $y=0$ (b)(i) $4$ (b)(iii) $x=2$ or $x=-3$

2025 JPJC P1 Q5

2025 JPJC P1 Q5

Video Solution:

Solution:

Solution locked