   Chapter 10.1, Problem 16E

Chapter
Section
Textbook Problem

# Finding an Equation of a Parabola In Exercises 15–22, find an equation of the parabola.Vertex: (–2, 1)Focus: (–2, –1)

To determine

To calculate: The equation of parabola with vertex (2,1) and focus (2,1).

Explanation

Given:

The vertex of parabola is (2,1) and its focus is (2,1).

Formula used:

The standard equation of a parabola with vertex (h,k) and directrix y=kp on a vertical axis is given by:

(xh)2=4p(yk).

And the coordinates of focus are:

(h,k+p).

Calculation:

Since, the focus of the parabola is (2,1) which is in third quadrant, so it must be a downward parabola, that is, its axis must be vertical.

Now, the standard equation of a parabola with vertex (h,k) and directrix y=kp on a vertical axis is given by:

(xh)2=4p(yk) …… (1)

And the coordinates of focus is:

(h,k+p) …… (2)

Now, the focus of the parabola is (2,1)

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