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