UPSC NDA Math Model Paper 10

Consider the parabola y2=−4ax
We want to replace the variables x and y by the parameter t.
We see that the LHS is a square.
⇒ When x is parameterised, the RHS should become a perfect square.
⇒ The parameterised form of x should be −at2
y2=−4ax
⇒y2=−4a(−at2)
⇒y2=4a2t2
⇒y=2at.
⇒ The parameterised form of y should be 2 at.
Hence, the parametric coordinate of any point of the parabola y2=−4ax is (−at2,2at)