Question

Find the equation of the cubic curve whose asymptotes are $x+a=0,y-a=0,x+y+a=0$ and which touches the $x$ axis at origin and passes through the point $(-2a,-2a)$?

• A. $xy(x+y)+a(y^2+xy-x^2)-10a^{2}y=0$
• B. $xy(x-y)+a(y^2+xy-x^2)+10a^{2}y=0$
• C. $xy(x+y)-a(y^2+xy-x^2)+10a^{2}y=0$
• D. None of these

Answer 1

The correct option is A $xy(x+y)+a(y^2+xy-x^2)-10a^{2}y=0$

So to find equation of cubic curve whose asymptotes are $x+a=0,y-a=0,x+y+a=0$

And which toches the x-axis at the origun nd passes through the point $(-2a,-2a)$

Put the given equation in options

For $x+a=0,y-a=0,x+y+a=0$ and

At point $(0,0)and(-2a,-2a)$ satisfy equation $\left(A\right)$

Cubic equation will be $xy(x+y)+a(y^2+xy-x^2)-10a^{2}y=0$