Question

Find all points having an x−coordinate of -4 whose distance from the point (4, 2) is 10.

Answer 1

`The\ distance\ between\ A(x_A;\ y_A)\ and\ B(x_B;\ y_B):\\\\d=√((x_B-x_A)^2+(y_B-y_A)^2)\\\\------------------------------\\\\A(-4;\ y);\ B(4;\ 2);\ d=10\\\\subtitute\\\\√((4-(-4))^2+(2-y)^2)=10\\\\√(8^2+(2-y)^2)=10\\\\√(64+(2-y)^2)=10\Rightarrow64+(2-y)^2=10^2\\\\64+(2-y)^2=100\ \ \ \ |subtract\ 64\ from\ both\ sides\\\\(2-y)^2=36\iff2-y=-√(36)\ or\ 2-y=√(36)\\\\2-y=-6\ or\ 2-y=6\ \ \ \ |subtract\ 2\ from\ both\ sides\\\\-y=-8\ or\ -y=4\ \ \ |change\ the\ signs\\\\y=8\ or\ y=-4`


`Answer:\boxed{(-4;\ 8)\ and\ (-4;-4).}`