   Chapter 10, Problem 15RE

Chapter
Section
Textbook Problem

# Finding the Standard Equation of a Parabola In Exercises 15 and 16, find the standard form of the equation of the parabola with the given characteristics.Vertex: (7, 0) x = 5

To determine

To calculate: The equation of parabola whose vertex is at (0,2) and equation of directrix is x=3.

Explanation

Given:

The coordinates of vertex are (0,2) and equation of directrix is x=3.

Formula used:

Equation of parabola is (yk)2=4p(xh) where (x,y) are arbitrary points, (h,k) is the vertex, and p is the focus.

The property, (ab)2=a22ab+b2.

Calculation:

Consider coordinates of vertex and equation of directrix which are (0,2) and x=3 respectively.

As the directrix is a vertical line on the left side of the graph and vertex lies on positive y-axis, so it is a upward parabola.

Hence, the focus is 3.

Recall the equation of parabola,

(yk)2=4p(xh), where (x,y) are arbitrary points, (h,k) is the vertex, and p is the focus

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