Find all y such that the distance between the points (4, 3) and (8, y) is 11.

Answer 1

you need

√((8-4)^2 + (y-3)^2) = 11
√(16+(y-3)^2) = 11
16+(y-3)^2 = 121
(y-3)^2 = 105
y-3 = ±√105
y = 3±√105

you can check this by noting that the locus of all points a distance of 11 from (4,3) is a circle:

(x-4)^2 + (y-3)^2 = 121
Now pick x=8, and see where y is
You end up doing exactly the same steps as shown above.