Step 1 The given parametric equations are \(x = 2t − 3t2\)

\(y = t2 − 3t\) Vertical tangent: It occurs when derivative is undefined for given parametric equations. Step 2 Solve the equations to find derivative with respect to t \(\frac{dx}{dt} = 2 - 6t\)

\({dy}{dt} = 2t - 3\)

\(\frac{dy}{dx} = \frac{dy}{dt} = (\frac{dt}{dx})\)

\(= \frac{2t-3}{2-6t}\) Now, the derivative is undefined when denominator of the above equation becomes zero i.e. \(2 − 6t = 0\)

\(2 = 6t\)

\(t = \frac{2}{6} = \frac{1}{3}\) Answer: Hence, for the given parametric equations , the vertical tangent is at \(t = \frac{1}{3}\) and option (a) is correct answer.