The video tutorial explains how to write the equation of a parabola given its focus and directrix. It begins by introducing the concept of a parabola and its defining properties. The instructor then demonstrates how to plot the focus and directrix to determine the vertex, which is crucial for writing the equation. The importance of the vertex is highlighted, and the standard form of the parabola equation is derived using the vertex and focus. The tutorial concludes with a summary of the steps involved in writing the equation.

What is the relationship between the focus, directrix, and any point on a parabola?

• The focus is always at the origin.

• The directrix is always a vertical line.

• The distance from the focus to the directrix is always zero.

• The distance from any point on the parabola to the focus is equal to the distance to the directrix.

Why is the vertex of a parabola important?

• It is equidistant from the focus and the directrix.

• It is the midpoint of the directrix.

• It is the point where the parabola intersects the x-axis.

• It is always located at the origin.

How do you determine the value of P in the parabola equation?

• By measuring the distance from the vertex to the x-axis.

• By measuring the distance from the vertex to the focus.

• By measuring the distance from the vertex to the directrix.

• By measuring the distance from the focus to the directrix.

What is the standard form of the equation for a parabola with a vertical axis?

• X - H = 4P(Y - K)^2

• X^2 = 4P(Y - K)

• Y - K = 4P(X - H)^2

• Y^2 = 4P(X - H)

How do you handle negative signs when substituting the vertex into the parabola equation?

• Use parentheses to correctly substitute negative values.

• Convert all negative values to positive.

• Add the negative signs to the equation.

• Ignore the negative signs.