Question

Find the real asymptotes of the curve x3+y3=3axy

Answer 1

Answer:

y= -x-a = -(x+a)  

Step-by-step explanation:

x³+y³-3axy = 0           ...(1)

The coefficient of the highest power x³ of x is 1 which is a constant .

so, there is no asymptote parallel to x- axis

The coefficient of the highest power y³ of y is 1, which is a constant.

so, there is no asymptote parallel to y-axis

Now ,

Putting x=1 ,y= m in the 3rd, 2nd, 1st degree terms of equation (1)

0³(m)= x³ + y³

0³(m) = 1+m³

O²(m) = -3axy

0²(m) = -3am

For slope O³(m) = 0

1+m³= 0

m= -1

where m= -1 , c= -a

so, y= mx+c

y= -x-a = -(x+a)              is the asymptote of the given curve