The diagram shows the curve with equation ${{x}^{3}}{{y}^{2}}+{{x}^{2}}{{y}^{3}}=1$. The curve is

Question

The diagram shows the curve with equation ${{x}^{3}}{{y}^{2}}+{{x}^{2}}{{y}^{3}}=1$. The curve is symmetrical about the line $y=x$ and has a stationary point $A$. Find the exact coordinates of $A$.[5] The point $B$ is the point of the curve at which the tangent is parallel to the $y$-axis. Hence, or otherwise, state the exact coordinates of $B$.[1]

Accepted Answer

(i) $A=\left(-\sqrt[5]{\frac89},\frac32\sqrt[5]{\frac89}\right)$ (ii) $B=\left(\frac32\sqrt[5]{\frac89},-\sqrt[5]{\frac89}\right)$

2015 SAJC P1 Q4

2015 SAJC P1 Q4

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