The curve described parametrically by , represents
- A.a pair of straight lines
- B.an ellipse
- C.a parabola
- D.a hyperbola
Show answer and solution
Correct option: C
Solution
From the parametric equations: x + y = 2t² + 2 and x - y = 2t. So t = (x - y)/2, and substituting into x + y = 2t² + 2 gives x + y = (x - y)²/2 + 2, i.e., (x - y)² = 2(x + y) - 4 = 2(x + y - 2). This is of the form X² = 2Y after rotating/translating axes, which is a parabola (one squared linear combination equals another linear combination).
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