Find the Properties y^2=-20x

Problem

y2=−20*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 y2=4*p*x Because the x term is linear and the coefficient is negative, the parabola opens to the left along the xaxis.

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

4*p=−20

p=−5

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

Vertex=(0,0)

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

Focus=(−5,0)

6. Identify the directrix. The directrix is a vertical line defined by x=−p

x=−(−5)

x=5

7. Find the axis of symmetry. The parabola is symmetric about the horizontal line passing through the vertex.

Axis of Symmetry:y=0

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

Latus Rectum Length=|−20|=20

Final Answer

Properties of *y2=−20*x:Vertex *(0,0),Focus *(−5,0),Directrix *x=5,Axis of Symmetry *y=0

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