Question

Raj tested hist new flashlight by shining it on his bedroom wall. The beam of light can be described by his equation x^{2}+y^{2}-2x-4y-31=0. How many inches wide is the beam of light on the wall?

Answer 1

Diameter=12 inches

Explanation:

Given:

x^{2}+y^{2}-2x-4y-31=0

Using completing the square

x^2 - 2x + 1 + y^2 - 4y + 4 = 31+1+4

(x-1)^2 + (y-2)^2 = 36

Rewrite in the form

(x-h)^2+(y-k)^2=r^2

We have,

(x-1)^2+(y-2)^2=6^2

radius = 6

Diameter =radius ×2

=6 × 2

diameter = 12 inches