Find the Properties y^2=12x

Problem

y2=12*x

Solution

1. Identify the form of the parabola. The equation y2=12*x is in the standard form y2=4*p*x which represents a parabola opening to the right with its vertex at the origin.

2. Determine the value of p By comparing y2=12*x to y2=4*p*x we set 4*p=12

3. Solve for p

4*p=12

p=3

4. Find the vertex. Since the equation is in the basic form y2=4*p*x the vertex is at the origin.

Vertex=(0,0)

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

Focus=(3,0)

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

Directrix:x=−3

7. Find the axis of symmetry. Since the parabola opens horizontally and the vertex is at (0,0) the axis of symmetry is the x-axis.

Axis of Symmetry:y=0

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

Latus Rectum Length=|12|=12

Final Answer

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

Want more problems? Check here!