Find the Properties y^2=20x

Problem

y^2=20*x

Solution

1. Identify the type of conic section. The equation is in the form y^2=4*p*x which represents a parabola opening to the right with its vertex at the origin (0,0)

2. Determine the value of p by comparing the given equation y^2=20*x to the standard form y^2=4*p*x

4*p=20

p=5

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

Focus=(5,0)

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

x=−5

5. Identify the axis of symmetry. Since the y term is squared, the parabola is symmetric about the x-axis.

y=0

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

Length=|20|=20

Final Answer

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

Want more problems? Check here!