Question

The line which is parallel to the X-axis and crosses the curve y=√(x) at an angle 45^∘, is

• A. \(x=\frac14\)
• B. \(y=\frac14\)
• C. \(y=\frac12\)
• D. y=1

Hint:

Angle of intersection = angle of tangent.

Answer 1

The Correct Option is C

Angle between curve and x-axis equals angle of tangent:
\( \dfrac{dy}{dx} = \dfrac{1}{2\sqrt{x}} = \tan 45^\circ = 1 \)
\( \Rightarrow \sqrt{x} = \dfrac{1}{2} \)
\( y = \sqrt{x} = \dfrac{1}{2} \)