BITSAT 2015 Paper

Given equation of a line parallel to X-axis isy = k.
Given equation of the curve is y = √x
On solving equation of line with the equation of curve, we get x = k2
Thus the intersecting point is (k2, k)
It is given that the line y = k intersect the curve y = √x at an angle of π/4. This means that the slope of the tangent to
y = √x at (k2,k) is tan (±

π

4

) = ± 1
⇒ (

dy

dx

)(k2,k) = ± 1 ⇒ (

1

2√x

)(k2,k) = ± 1
⇒ k ±

1

2