Question

The parametric coordinate of any point of the parabola y2 = -4ax is
1. (-at², -2at)
2. (-at², 2at) 
3. (a sin2 t, -2a sin t)
4. None of these

Answer 1

Correct Answer - Option 2 : (-at², 2at) 

Calculations:

Consider the parabola y2 = -4axy2=4ax.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 2at.

Hence, the parametric coordinate of any point of the parabola y2 = -4ax is (-at², 2at).