Find the Properties y^2=-16x

Problem

y2=−16*x

Solution

1. Identify the form of the parabola. The equation y2=−16*x is in the standard form y2=4*p*x which represents a parabola that opens horizontally.

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

4*p=−16

p=−4

3. Find the vertex. Since the equation is in the form y2=4*p*x with no translations, the vertex is at the origin.

Vertex=(0,0)

4. Calculate the focus. For a horizontal parabola, the focus is located at (p,0)

Focus=(−4,0)

5. Identify the directrix. The directrix is a vertical line given by the equation x=−p

x=−(−4)

x=4

6. Determine the axis of symmetry. Since the parabola opens horizontally and the vertex is at the origin, the axis of symmetry is the x-axis.

y=0

7. Find the length of the latus rectum. The length is given by |4*p|

Length=|−16|=16

Final Answer

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

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