Question

What are the tangents to the curve x^3+ y^3=3axy at the origin?

(a) x=0

(b) x=0, y=0

(c) y=0

(d) x=y

I had been asked this question in an interview for job.

Question is from Curves in Cartesian Form in chapter Curve Tracing of Engineering Mathematics

Answer 1

The correct answer is (b) x=0, y=0

For explanation I would say: Given: x^3+ y^3=3axy

To find the tangent to the curve at the origin, we need to equate the lowest degree term to 0.

Therefore, 3axy=0, which gives x=0 and y=0 as two tangents to the curve at origin.