The curve $C$ has equation \({\frac{{{\left( x+1 \right)}^{2}}}{4}+\frac{{{\left( y+3 \right)}^{2}

Question

The curve $C$ has equation ${\frac{{{\left( x+1 \right)}^{2}}}{4}+\frac{{{\left( y+3 \right)}^{2}}}{10}=1}$. Sketch $C$,[3] Hence state the range of positive values of $k$ such that ${{\left( x-5 \right)}^{2}}+{{\left( y+3 \right)}^{2}}={{k}^{2}}$ intersects $C$ at least once.[2]

Accepted Answer

(i) Centre $(-1,-3)$, horizontal semi-axis $2$, vertical semi-axis $\sqrt{10}$ (ii) $4\le k\le8$

Graphing Techniques - Graphs of Conic Sections

Graphing Techniques - Graphs of Conic Sections

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