The equation of a curve is given by $xy-2{{y}^{2}}+4{{x}^{2}}=66$. Find the exact coordinates of the

Question

The equation of a curve is given by $xy-2{{y}^{2}}+4{{x}^{2}}=66$. Find the exact coordinates of the points on the curve where the tangent is parallel to the $y$-axis. [4] Show that every line parallel to the $x$ -axis cuts the curve at two distinct points. [3]

Accepted Answer

(i) $(4,1)$ and $(-4,-1)$; (ii) every line parallel to the $x$-axis cuts the curve at two distinct points

2012 IJC P1 Q4

2012 IJC P1 Q4

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