The GATE Grind

GATE 2026 IN – Question 53

Engineering Mathematics · Calculus and vector calculus · 2 marks · Multiple select

Given $f(x,y)=x^2-2xy+y^2$, the complete contour of the equation $f(x,y)=1$ is described by the option(s) ________.

  1. A line, $x-y=1$
  2. A circle with radius 1
  3. An ellipse with length of major axis equal to 1
  4. A line, $x-y=-1$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) A line, $x-y=1$; (D) A line, $x-y=-1$

Explanation

Factor the quadratic as $f(x,y)=(x-y)^2$. The level-set condition is $(x-y)^2=1$, equivalent to $x-y=1$ or $x-y=-1$.

The complete contour is the union of these two parallel lines. Select **A and D**.