The equation of a curve is $2xy + (1 + y)^2 = x$. Find the equations of the two tangents which are

Question

The equation of a curve is $2xy + (1 + y)^2 = x$. Find the equations of the two tangents which are parallel to the $y$-axis.[4] The normal to the curve at the point $A(-4, 5)$ meets the curve again at the point $B$. Find the coordinates of point $B$.[4]

Accepted Answer

(i) $x=0$ and $x=-3$ (ii) $\displaystyle B\left(-\frac{1225}{88},\frac{13}{22}\right)\approx(-13.9,0.591)$ (3 s.f.)

2024 MI P1 Q4

2024 MI P1 Q4

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