Problem Statement:
Find the coordinates of the point on the curve √x * √y = 4 at which the tangent is equally inclined to the Axes.

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Understanding the Problem:
To find the point on the curve where the tangent is equally inclined to the Axes, we need to determine the slope of the tangent at that point and check if it is equal to ±1.

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Solution:
- Let's first differentiate the given equation √x * √y = 4 with respect to x.
- We get: (1/2√y) * √x + (1/2√x) * √y(dy/dx) = 0
- Simplifying, we get: x/y + y/x(dy/dx) = 0
- Solving for dy/dx, we get: dy/dx = -y/x * (x/y) = -1
- This represents the slope of the tangent at the point of interest.
- Since the slope is -1, the tangent is equally inclined to the X-axis and Y-axis.
- Now, we substitute this slope back into the original equation and solve for x and y.
- √x * √y = 4
- √x * √(-x) = 4
- x = 4^2 = 16
- Since y = 16, the coordinates of the point on the curve where the tangent is equally inclined to the Axes are (16, 16).
Therefore, the coordinates of the point on the curve √x * √y = 4 at which the tangent is equally inclined to the Axes are (16, 16).