Question

Find the sum of all values of a such that the point (a,7) is 3 sqrt 5 from the point (2,1).

Answer 1

up to the left, and up to the right

d^2 = (2-a)^2 + (1-7)^2

d^2 = 45 = 4 - 4 a + a^2 + 36

5 = a^2 - 4 a

a^2 - 4 a - 5 = 0

(a-5)(a+1) = 0

a = 5 or a = -1

Answer 2

Or, you can think of it as looking for the intersections of a circle and a line.

The circle: (x-2)^2 + (y-1)^2 = 45
The line: y=7

They intersect where

(x-2)^2 + (7-1)^2 = 45

now the math proceeds as above