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Chapter 7: Problem 69

What is a parabola?

Short Answer

Expert verified
A parabola is a U-shaped, symmetric curve on a plane, described by the equation \(y = ax^2 + bx + c\). All points on the parabola are equidistant from a point called the focus and a line called the directrix.

Step by step solution

01

Definition

A parabola is a U-shaped symmetrical curve on a plane. It can be categorized into different parts: vertex, axis of symmetry, focus, and directrix.
02

Mathematical Representation

A parabola can be mathematically represented in the form \(y = ax^2 + bx + c\) where \(a\), \(b\), and \(c\) are constants.
03

Properties of Parabola

Some important properties of a parabola include that it is symmetric with respect to its vertical axis, the vertex represents the minimum or maximum point, all points on the parabola are equidistant from the focus and the directrix.

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I noticed that depending on the values for \(A\) and \(B\), assuming that they are both not zero, the graph of \(A x^{2}+B y^{2}=C\) can represent any of the conic sections other than a parabola.

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((-3,4)\); Directrix: \(y=2\)

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$8 y^{2}+4 x=0$$

Will help you prepare for the material covered in the next section. Divide both sides of \(4 x^{2}-9 y^{2}=36\) by 36 and simplify. How does the simplified equation differ from that of an ellipse?

Describe how to graph \(\frac{x^{2}}{9}-\frac{y^{2}}{1}=1\)
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