Find the co-ordinates of the point on the curve at which tangent is equally inclined to the axes.

Given: curve √x+√y = 4

To find: the co-ordinates of the point on the curve at which tangent is equally inclined to the axes

Explanation: given √x+√y = 4

Now differentiating this with respect to x, we get

Applying the sum rule of differentiation, we get

Applying the differentiation, we get

This is the tangent to the given curve.

Now it is given that the tangent is equally inclined to the axes,

∴ y = x……….(ii)

Substituting equation (ii) in the curve equation, we get

√y+√y = 4

2√y = 4

√y = 2

⇒ y = 4

When y = 4, then x = 4 from equation (ii)

So the co-ordinates of the point on the curve √x+√y = 4 at which tangent is equally inclined to the axes is (4,4).