Question

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

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Solution

## Let the required point be (x1,y1)Given equation of curve is √x+√y=4Since (x1,y1) lies on the curve we get,⇒√x1+√y1=4 ...(1)Consider the curve √x+√y=4On differentiating w.r.t x we get⇒12√x+12√ydydx=0⇒dydx=−√yxGiven that tangent is equally inclined to the axesθ=450 ⇒tanθ=1⇒(dydx)(x1,y1)=1⇒−√y1x1=1Squaring on both sides, we get⇒x1=y1From (1) we have ⇒√x1+√y1=4 ⇒√x1+√x1=4 ⇒2√x1=4 ⇒√x1=2 ⇒√x1=2 ⇒x1=y1=4 Hence the required point is (4,4)

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