Find the Properties y^2=-5x

Problem

y2=−5*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 its coefficient is negative, the parabola opens to the left along the xaxis.

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

4*p=−5

p=−5/4

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

(0,0)

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

Focus=(−5/4,0)

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

x=5/4

7. Identify the axis of symmetry. The parabola is symmetric about the xaxis:

y=0

Final Answer

Vertex: *(0,0), Focus: *(−5/4,0), Directrix: *x=5/4, Axis of Symmetry: *y=0

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