Question

Which of the following points lie on the parabola x² = 4ay? 

Options

• x = at², y = 2at 

• x = 2at, y = at² 

• x = 2at², y = at 

   

• x = 2at, y = at² 

Answer 1

 x = 2at, y = at² 

^{Substituting x = 2at, y = at2 in the given equation:} 

^{\[\left( 2at \right)^2 = 4a\left( a t^2 \right)\]
\[ \Rightarrow 4 a^2 t^2 = 4 a^2 t^2\]}

^{Hence, (2at, at2) lies on the parabola x2 = 4ay.}