#### Question

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

#### Solution

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} = 4*ay* or

*x*^{2 }= – 4*ay*.

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} = –4*ay*.

Here, *a* = 3

Thus, the equation of the parabola is *x*^{2} = –12*y*.

Is there an error in this question or solution?

Solution Find the Equation of the Parabola that Satisfies the Following Conditions: Focus (0, –3); Directrix Y = 3 Concept: Parabola - Standard Equations of Parabola.