2006 CJC Promo [Modified]
2006 CJC Promo [Modified]
3 marks
Promo
Find the Cartesian equations and coordinates of the intersections of the following curve with the \(x\) and \(y\)-axes (if any)
\(x=\sqrt{{{t}^{4}}+1}\), \(y={{t}^{2}}\), \(t\in \mathbb{R}\)
Sketch the curve, indicating clearly the equation of any asymptote(s) and coordinates of any axial intercept(s).[3]
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Answer:Cartesian: \(x = \sqrt{y + 1}\), \(y \geq 0\), \(x \geq 1\); x-intercept: \((1, 0)\)
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