The GATE Grind

GATE 2016 CE (CE2) – Question 38

Engineering Mathematics · Calculus: Limits, continuity, mean value theorems, maxima and minima, Taylor series · 2 marks · Multiple choice

The intersection angle of $x^2=4y$ and $y^2=4x$ at $(0,0)$ is ______.

  1. 0°
  2. 30°
  3. 45°
  4. 90°

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Show answer and explanation

Correct answer: (D) 90°

Explanation

For x²=4y, write y=x²/4; its tangent at the origin is horizontal. For y²=4x, write x=y²/4; its tangent at the origin is vertical. The two tangents are perpendicular, so the angle is **90°, D**. This avoids dividing by a zero derivative.