1. The problem states that the parabola is given by the parametric equations $x=at^2$ and $y=2at$. 2. We want to show that these parametric equations represent the parabola $y^2=4ax$. 3. From the second equation, solve for $t$: $$t=\frac{y}{2a}$$ 4. Substitute this expression for $t$ into the first equation: $$x = a\left(\frac{y}{2a}\right)^2 = a \frac{y^2}{4a^2} = \frac{y^2}{4a}$$ 5. Multiply both sides by $4a$ to get: $$4ax = y^2$$ 6. This matches the standard form of the parabola equation: $$y^2 = 4ax$$ Therefore, the parametric equations $x=at^2$ and $y=2at$ represent the parabola $y^2=4ax$.