A curve $C$ has equation $x^2 y^2 + 3xy + 2y^2 - x - 2 = 0$. Find \(\frac{\mathrm{d}y}{\mathrm{d

Question

A curve $C$ has equation $x^2 y^2 + 3xy + 2y^2 - x - 2 = 0$. Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ and $y$.[3] Find the gradients of the tangents at $x = 0$.[2] Using an algebraic method, show that there is no part of the curve for which $x < -4$.[3]

Accepted Answer

(i) $\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{1-3y-2xy^2}{2x^2y+3x+4y}$ (ii) $-\dfrac12$ and $-1$ (iii) No part of the curve exists for $x<-4$

2024 NJC Promo Q6

2024 NJC Promo Q6

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