Question

# Find the coordinates of the point on the curve √x+√y=4 at which tangent is equally inclined to the axes.

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Solution

## We have√x+√y=4⇒x12+y12=4⇒12.1x12+12.1Y12.dydx=0∴dydx=−12.x−122.y12=−√yx Since, tangent is equally inclined to the axes. ∴dydx=±1⇒−√yx=±1⇒yx=1⇒y=xFrom Eq.(i).,√y+√y=4⇒2√y=4⇒4y=16∴y=4 and x=4 So, the required coordinates are (4, 4).

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