Question

Find the equation of the normal to the curve x³ + y³ = 8xy at the point where it meets the curve y² = 4x other than origin.

Answer 1

Given curves are

x³ + y³ = 8xy and y² = 4x

On solving, we get, x = 0, 4

when x = 0, then y = 0

when x = 4, then y = ± 4

Thus, the points are (0, 0), (4, – 4), (4, 4)

But (4, – 4) does not satisfy the equations

Hence, the required point is (4, 4)

Now, x³ + y³ = 8xy

Hence, the equation of the normal is

y – 4 = 1(x – 4)

⇒ x – y = 0