What do you need to know to write the equation of a parabola for conic sections

The video tutorial explains how to write the equation of a parabola using information such as the focus, directrix, and vertex. It emphasizes understanding the relationships between these elements to determine the value of P, which is crucial for forming the equation. The tutorial also covers different forms of parabola equations based on their axis of symmetry, whether vertical or horizontal. By dissecting the provided information and applying it to the correct equation form, learners can accurately write parabola equations.

What are the key elements needed to write the equation of a parabola?

• Focus, directrix, and vertex

• Length and width

• Radius and diameter

• Slope and intercept

How is the value of P determined in the context of a parabola?

• By finding the midpoint of the directrix

• By calculating the area of the parabola

• By measuring the distance between two points

• By understanding the relationship between the vertex, focus, and directrix

What is the vertex form of a parabola?

• (M, N)

• (X, Y)

• (H, K)

• (A, B)

Which type of parabola opens up or down?

• Parabolas with a horizontal axis of symmetry

• Parabolas with a vertical axis of symmetry

• Parabolas with no axis of symmetry

• Parabolas with a diagonal axis of symmetry

What is the equation for a parabola with a horizontal axis of symmetry?

• H - K = 4P

• X + Y = 4P

• X - H^2 = 4P(Y - K)

• Y - K^2 = 4P(X - H)