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Chapter 11: Problem 22

Find an equation of the following parabolas, assuming the vertex is at the origin. A parabola with focus at (-4,0)

Short Answer

Expert verified
Answer: x = -16y^2

Step by step solution

01

Determine the orientation of the parabola

The vertex of the parabola is at the origin (0,0), and the focus is at (-4,0). Since the focus is to the left of the vertex, the parabola will open to the left (which is negatively on the x-axis).
02

Find the distance from the vertex to the focus (p)

The vertex and the focus are only separated along the x-axis. Therefore, we can find the distance between them by finding the difference between the x-coordinates of the vertex and the focus. The distance p is given by: p = |0 - (-4)| = 4
03

Write the equation of the parabola using the standard formula

Since the parabola opens to the left (on the negative x-axis), its standard equation is given by x = -4py^2, where p is the distance between the vertex and the focus. Substituting the value of p, we get: x = -4(4)y^2 x = -16y^2 So, the equation of the parabola with the vertex at the origin and the focus at (-4,0) is x = -16y^2.

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