Question

Find the equation of the normal to the curve x + y = x^y, where it cuts the x-axis.

Answer 1

The equation of the given curve is

x + y = x^y

put y = 0, then x = 1.

So, the point is (1, 0)

Now, x + y = x^y

⇒ Slope of normal = 1

Hence, the equation of the normal is

y – 0 = 1 (x – 1)

⇒ y = x – 1.