Understanding Parabolas

Parabolas are fundamental conic sections used in physics, engineering, and mathematics. They describe projectile motion, satellite dish shapes, and optimal structural designs.

Calculation Steps

Determine orientation (vertical/horizontal)
Identify vertex coordinates (h,k)
Calculate focus using p-value
Calculate directrix line equation
Verify using standard form equation

Practical Examples

For a satellite dish with focal length 2m and vertex at (0,0): p=2, focus at (0,2), directrix at y=-2

Parameter	Vertical Parabola	Horizontal Parabola
Standard Form	(x-h)² = 4p(y-k)	(y-k)² = 4p(x-h)
Focus	(h, k+p)	(h+p, k)

Tip: Always verify your p-value sign - positive for upward/right opening, negative for downward/left opening.

Frequently Asked Questions

What does the p-value represent?

The p-value represents the distance between the vertex and focus (and vertex and directrix). It determines the "width" of the parabola.

Can a parabola open left or down?

Yes - use a negative p-value for downward opening vertical parabolas or leftward opening horizontal parabolas.

How accurate are the calculations?

Calculations are mathematically precise. Ensure you input valid numerical values for correct results.

Parabola Calculator - Focus Directrix Vertex

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Parabola Calculator - Focus Directrix Vertex

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