Find the Properties y^2=-8x

Problem

y^2=−8*x

Solution

1. Identify the type of conic section. Since only one variable is squared, the equation represents a parabola.

2. Determine the orientation. The equation is in the form y^2=4*p*x Because the x term is linear and has a negative coefficient, the parabola opens to the left along the xaxis.

3. Calculate the value of p Set 4*p equal to the coefficient of x

4*p=−8

p=−2

4. Find the vertex. Since there are no h or k shifts in the equation y^2=−8*x the vertex is at the origin.

Vertex=(0,0)

5. Determine the focus. The focus is located at (p,0) for a parabola opening horizontally.

Focus=(−2,0)

6. Determine the directrix. The directrix is a vertical line given by x=−p

x=−(−2)

x=2

7. Identify the axis of symmetry. The axis of symmetry is the line that passes through the vertex and focus, which is the xaxis.

y=0

8. Calculate the focal diameter (length of the latus rectum). This is the absolute value of 4*p

|4*p|=|−8|=8

Final Answer

y^2=−8*x⇒Vertex: *(0,0), Focus: *(−2,0), Directrix: *x=2, Axis of Symmetry: *y=0

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