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

Question

The curve $C$ has equation ${\frac{{{\left( x-1 \right)}^{2}}}{2}-{{\left( y+2 \right)}^{2}}=1}$. Sketch $C$, stating the equations of the asymptotes and their point of intersection.[3] Hence state the exact range of values of $m$ such that the straight line $y=m\left( x-1 \right)-2$does not intersect $C$.[2]

Accepted Answer

(i) Asymptotes $y+2=\pm\dfrac{x-1}{\sqrt2}$, intersecting at $(1,-2)$ (ii) $m\le-\dfrac1{\sqrt2}$ or $m\ge\dfrac1{\sqrt2}$

Graphing Techniques - Parameter Conditions for Graphs and Equations

Graphing Techniques - Parameter Conditions for Graphs and Equations

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