Question

The parametric equations (2+t², 2t+1) represent

• A. A parabola with focus at (2, 1)
• B. A parabola with vertex at (2, 1)
• C. An ellipse with centre at (2, 1)
• D. A hyperbola with centre at (2, 1)

Answer 1

Answer: (B)

A parabola with vertex at (2, 1)

Answer 2

Let x = 2+t²,y = 2t + 1

ie., t² = x – 2, t = $\frac{y - 1}{2}$

⇒ $\left( \frac{y - 1}{2} \right)^{2} = (x - 2)$

⇒ (y-1)² = Q(x-2) is a parabola with vertex (2, 1).