Question

The equation of tangent to the curve $x{y}^3+x^{2}y+2x^2+3y-2x=0$ at origin, is

• A. $x=0$
• B. $y=0$
• C. $3y-2x=0$
• D. $2y-3x=0$

Answer 1

The correct option is C $3y-2x=0$

Given curve : $x{y}^3+x^{2}y+2x^2+3y-2x=0,$
As, point $(0,0)$ lies on the given curve.
$\Rightarrow$ Tangent at origin will be directly determined by equating the lowest degree term to $0.$
$\therefore$ Equation of tangent will be $3y-2x=0$