Question:
The line which is parallel to X-axis and crosses the curve \(y=\sqrt{x}\) at an angle \(45^\circ\) is
The line which is parallel to X-axis and crosses the curve \(y=\sqrt{x}\) at an angle \(45^\circ\) is
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Angle of tangent gives slope directly.
Updated On: Mar 23, 2026
- \(x=\frac14\)
- \(y=\frac14\)
- \(y=\frac12\)
- \(y=1\)
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Slope of curve: \[ \frac{dy}{dx}=\frac{1}{2\sqrt{x}} \]
Step 2: Angle between tangent and x-axis is \(45^\circ\): \[ \tan45^\circ=1=\frac{1}{2\sqrt{x}} \Rightarrow x=\frac14 \]
Step 3: \[ y=\sqrt{\frac14}=\frac12 \]
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