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Single Variable Calculus

8th Edition
James Stewart
ISBN: 9781305266636

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BuyFindarrow_forward

Single Variable Calculus

8th Edition
James Stewart
ISBN: 9781305266636
Textbook Problem

A cross-section of a parabolic reflector is shown in the figure. The bulb is located at the focus and the opening at the focus is 10 cm.

  1. (a) Find an equation of the parabola.
  2. (b) Find the diameter of the opening |CD|, 11 cm from the vertex.

images

a)

To determine

To Find: The equation of the parabola.

Explanation

Given:

The parabola appears as drawn in the below figure.

The opening at the focus is 10cm and distance from the vertex to the CD is 11cm .

Calculation:

Referring to the figure (1), the focus and the vertex are located in the x axis.

The standard equation the parabola is as below.

y2=4px (1)

The focus of the parabola is of the form (p,0) .

Referring to the figure (1) at the point A , the focus of the parabola is (p,5) .

Substitute the value (p,5) for (x,y) in equation (1), to find the value p

b)

To determine

To Find: The diameter of the opening CD.

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