Question

Find the equation of the tangent and normal drawn to the curve y⁴ - 4x⁴ - 6xy = 0 at the point M (1, 2).

Answer 1

y⁴ - 4x⁴ - 6xy = 0

Differentiating both sides w.r.t. x, we get

= slope of the tangent at (1, 2) 

∴ the equation of normal at M (1, 2) is

The slope of normal at (1, 2)

∴ the equation of normal at M (1, 2) is

Hence, the equations of tangent and normal are 14x – 13y + 12 = 0 and 13x + 14y – 41 = 0 respectively.