The distance between the points $A$ and $B$ is $\sqrt{34}.$ If $A = (a,4)$ and $B = (-20,33),$ then find the sum of all possible values of $a.$
This is impossible
(x + 20)^2 + (y - 33)^2 = 34 is a circle centered at ( -20, 33) with a radius of sqrt (34)
Every point on the line y = 4 is more than sqrt (34) units away from the center of this circle
See the graph below
+403 
