A circle has center (5, 8) and radius 2. Find all values of y such that (4, y) a point on the circle.

Question

A circle has center (5, 8) and radius 2. Find all values of y such that (4, y) a point on the circle. If there are two answers, enter the SMALLER answer in the first box and the LARGER answer in the second box

Answer 1

Distance formula:

sqrt( (5-4)^2 + (8-y)^2) = 2

sqrt( 1^2 + (8-y)^2) = 2

sqrt( 1 + 64 - 16y + y^2) = 2

sqrt( y^2 - 16y + 65) = 2

y^2 - 16y + 65 = 4

y^2 - 16y + 61 = 0

y = [ 16 +or- sqrt( 256 - 244)]/2

= [ 16 +or- 2*sqrt(3)]/2