Question

Trace the curve y²(2a - x) = x³, a > 0.

Answer 1

Note that the curve passes through the origin and is symmetrical about the x-axis.

y = x³/(2a - x)

LHS is positive. If x is negative or if x is greater than 2a, RHS becomes negative. Hence the curve lies only in the interval 0 to 2a. When x → 2a, y → ∞. Therefore, the line x = 2a is an asymptote for the curve. A rough figure is shown (Fig.).