Find the Properties y^2=24x

Problem

y2=24*x

Solution

1. Identify the form of the parabola. The equation y2=24*x is in the standard form y2=4*p*x which represents a parabola that opens to the right with its vertex at the origin.

2. Determine the value of p by setting 4*p equal to the coefficient of x

4*p=24

p=6

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

Vertex=(0,0)

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

Focus=(6,0)

5. Determine the equation of the directrix. The directrix is a vertical line located at x=−p

x=−6

6. 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.

y=0

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

Length=|24|=24

Final Answer

Vertex: *(0,0), Focus: *(6,0), Directrix: *x=−6, Axis of Symmetry: *y=0, Latus Rectum Length: *24

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