The curve is called the folium of Descartes

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

The curve

y^{3}+3xy=x^{3}

is called the folium of Descartes. Find all point(s) on this curve where the tangent makes an angle of

45^{\circ}

with the positive

x

-axis.