Question

Find the equation of the parabola that satisfies the following conditions: Focus$(0, -3);$ directrix $y = 3$

Answer 1

Given that

Focus $= (0, -3);$ directrix y= 3 $$$ Since the focus lies on the y-axis, the y-axis is the axis of the parabola. Therefore, the equation of the parabola is either of the form x^2= 4ay$or$x^2 = - 4ay.$It is also seen that the directrix,$y= 3$is above the x-axis, while the focus$(0, -3)$is below the x-axis. Hence, the parabola is of the form$x^2= -4ay. $

Here,$a = 3$
Thus, the equation of the parabola is $x^2= -12y.$