[Math] Tangents to the curve and parallel to the $y$-axis

Question

The equation of a curve is $$3x^2 + 8xy + y^2 = -13.$$ Find the equations of the two tangents which are parallel to the $y$-axis.

Answer 1

Hints :

• differentiate (you should get a $f(x,y)dx+g(x,y)dy=0$ equation)
• search the zeros of $\frac {dx}{dy}$ (you should get $y$ in function of $x$)
• replace $y$ (for example) in the initial equation and solve