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Q)

The Asymptote x^3+y^3=3axy is find the equation

The Asymptote x^3+y^3=3axy is find the equation

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A)
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
 
 
Now ,
 
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 
 
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