Find the Properties y^2=28x

Problem

y2=28*x

Solution

1. Identify the form of the parabola. The equation y2=28*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=28

p=7

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=(7,0)

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

Directrix:x=−7

6. Identify the axis of symmetry. Since the y term is squared, the parabola is symmetric about the horizontal line passing through the vertex.

Axis of Symmetry:y=0

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

Length of Latus Rectum=|28|=28

Final Answer

Properties of *y2=28*x:Vertex *(0,0), Focus *(7,0), Directrix *x=−7, Axis of Symmetry *y=0

Want more problems? Check here!