Question

Trace the curve a y^2 = x^3​

Answer 1

Solution:

    The given curve is ay² = x³

Characteristic properties:

(i) The curve contains y². So the curve is symmetrical about x-axis, i.e., the curve is stretched on both sides of the x-axis in mirror identical.

(ii) This curve has no asymptote.

(iii) The curve passes through the origin (0, 0) and this is the only point where it meets the coordinate axes. In no other point, the curve cuts the axes.

(iv) From the given equation, we have y² = x³ / a,

i.e., y = ± x √x / √a. For real y we get x ≥ 0

Thus the graph of the given curve is given in the attached figure.