The curve $C$ has equation $\dfrac{(x-1)^2}{2} - (y+2)^2 = 1$. Sketch $C$, stating the equations of

Question

The curve $C$ has equation $\dfrac{(x-1)^2}{2} - (y+2)^2 = 1$. 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 $y = m(x-1) - 2$ does not intersect $C$. [2]

Accepted Answer

(i) Asymptotes: y = -2 ± (x-1)/√2 (ii) m ≥ 1/√2 	ext{ or } m ≤ -1/√2

Worked Example 3

Worked Example 3

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