The curve $C$ has equation ${\frac{{{\left( x-2 \right)}^{2}}}{2}+{{\left( y-3 \right)}^{2}}=1}$

Question

The curve $C$ has equation ${\frac{{{\left( x-2 \right)}^{2}}}{2}+{{\left( y-3 \right)}^{2}}=1}$. Sketch $C$,[3] Hence state the range of positive values of $k$ such that ${{\left( x-2 \right)}^{2}}+{{\left( y+3 \right)}^{2}}={{k}^{2}}$ intersects $C$ at twice.[2]

Accepted Answer

(i) Ellipse centred at $(2,3)$ with semi-axes $\sqrt2$ and $1$ (ii) $5<k<7$

Graphing Techniques - Graphs of Conic Sections

Graphing Techniques - Graphs of Conic Sections

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