Answer to Question #152382 in Calculus for Amlan bora

Question

Find the asymptotes parellel to the x and y axis of the curves ( x^3+y^3)y=bx^3

Answer 1

Given curve is ( x^3+y^3)y=bx^3

i.e. y⁴ + x³y - bx³ = 0

To find the asymptote parallel to y -axis we equate the coefficient of highest power of y to zero and to find the asymptote parallel to x -axis we equate the coefficient of highest power of x to zero.

In this curve highest power of y is 4 and its coefficient is 1. Also highest power of x is 3 and its coefficient is (y-b)

So for asymptote parallel to y-axis

1 = 0 which is absurd.

So no asymptote parallel to y-axis exist.

So for asymptote parallel to x-axis

y - b = 0

=> y = b

So asymptote parallel to x-axis is y = b