A parabola can be drawn given a focus of (4,-7) and a directrix y =5 . Write the equation of the parabola in any form.

Given that the focus is at (4,-7) and the directrix is at y=5.

The detailed article, * parabolic equations *Parabola Equation.Types of parabolic equations. can be reviewed for concepts on solving this problem step by step.

Let us follow the steps in the article to understand easy.

**Step1: Firstly, Identify the orientation of the focus point coordinate and the directrix line whether it is a horizontal or a vertical line.**

- The directrix line is the Horizontal dotted line y=5.and the focus is located below the directrix line.

**Step2: Find the vertex (h,k) by finding the mid-point of the focus point and the directrix line.**

- The “y” coordinate of the focus point (4,-7) is -7.So the vertical distance between the focus and the directrix is 7+5 = 12. Therefore the midpoint will be at a distance of 6 units from the focus. Hence (4 , -7+6) = (4 ,-1) is the vertex.

**Step2:Get the focal length “a” from the vertex calculated and the focal point.**

- The focal distance we just found as 6. This is the half way distance between the focus and directrix y=5

**Step4: If the directrix of the form Y= Constant number,( A horizontal line) then the parabola equation would be**

**1)(X-h)^2 = 4a(Y-k) (If the focus point is above the directrix line)**

**2)(X-h)^2=-4a(Y-k) (If the focus point is below the directrix line )**

- Since the focus point is below the directrix line, the vertex (h,k) is (4,-1) and the focal length is a= 6. The equation of the parabola would be
**(X-h)^2=-4ay = (x- 4)^2 =-4*6*(y- (-1))**

Therefore, the final solution would be