Find the Properties x^2=-16y

Problem

x2=−16*y

Solution

1. Identify the form of the parabola. The equation is in the form x2=4*p*y which represents a parabola that opens vertically.

2. Determine the value of p by setting the coefficient of y equal to 4*p

4*p=−16

p=−4

3. Find the vertex. Since there are no h or k offsets in the equation, the vertex is at the origin.

Vertex=(0,0)

4. Determine the direction of opening. Since p<0 and the equation is x2=4*p*y the parabola opens downward.

5. Calculate the focus. For a vertical parabola, the focus is at (0,p)

Focus=(0,−4)

6. Identify the directrix. The directrix is a horizontal line given by y=−p

y=−(−4)

y=4

7. Find the axis of symmetry. Since the parabola opens vertically and the vertex is at (0,0) the axis of symmetry is the yaxis.

x=0

8. Calculate the focal diameter (length of the latus rectum) using |4*p|

Focal Diameter=|−16|=16

Final Answer

Properties of *x2=−16*y:Vertex *(0,0),Focus *(0,−4),Directrix *y=4,Axis of Symmetry *x=0

Want more problems? Check here!