The curve $C$ is the translation of $\frac{{{x}^{2}}}{9}-{{y}^{2}}=1$ by one unit in the positive $x

Question

The curve $C$ is the translation of $\frac{{{x}^{2}}}{9}-{{y}^{2}}=1$ by one unit in the positive $x$-direction. Sketch the curve $C$, showing clearly the equations of asymptotes, axial intercepts and coordinates of turning points, if any. Given that $k$ is a positive constant and $C$ intersects the curve with equation ${{y}^{2}}+\frac{{{x}^{2}}}{{{k}^{2}}}=1$ at exactly two distinct points, state the range of values of $k$.

Accepted Answer

$2 < k < 4$

NJC Graphing Techniques Tutorial Q5

NJC Graphing Techniques Tutorial Q5

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