Which of the following equations represents a parabola

• Option A: (x − y)³ = 3
• Option B: x/y − y/x = 0
• Option C: x/y + 4/x = 0
• Option D: (x + y)² + 3 = 0

To determine which equation represents a parabola, let's analyze each option:

Option A: (x − y)³ = 3

This equation is a cubic equation, not a parabola.

Option B: x/y − y/x = 0

This can be rearranged to form a relationship between x and y, but it does not represent a parabola.

Option C: x/y + 4/x = 0

This equation can be manipulated, but it does not yield a parabolic form.

Option D: (x + y)² + 3 = 0

This equation cannot be satisfied for real numbers since the left side is always positive. It does not represent a parabola either.

Final Analysis

None of the provided options represent a parabola. A standard parabolic equation typically takes the form of y = ax² + bx + c or x = ay² + by + c.