Find the Properties y^2=3x

Problem

y2=3*x

Solution

1. Identify the type of conic section. Since the equation is in the form y2=4*p*x it represents a parabola that opens to the right with its vertex at the origin (0,0)

2. Determine the value of p by comparing the given equation y2=3*x to the standard form y2=4*p*x

4*p=3

p=3/4

3. Find the focus. For a parabola opening to the right, the focus is located at (p,0)

Focus=(3/4,0)

4. Find the directrix. The directrix is a vertical line given by the equation x=−p

Directrix:x=−3/4

5. Identify the axis of symmetry. Since the y term is squared and the vertex is at the origin, the axis of symmetry is the x-axis.

Axis of Symmetry:y=0

6. Calculate the length of the latus rectum. The length is given by |4*p|

Latus Rectum Length=3

Final Answer

Vertex: *(0,0), Focus: *(3/4,0), Directrix: *x=−3/4, Axis of Symmetry: *y=0

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