Question

Find all the points having an x-coordinate of 4 whose distance from the point (-2,-1) is 10

Answer 1

`A(x_1;\ y_1);\ B(x_2;\ y_2)\\\\the\ distance\ between\ A\ and\ B:\\\\d=√((x_2-x_1)^2+(y_2-y_1)^2)\\\\A(-2;-1);\ B(4;\ y);\ d=10\\\\subtitute\\\\√((4-(-2))^2+(y-(-1))^2)=10\\\\√((4+2)^2+(y+1)^2)=10\\\\√(6^2+(y+1)^2)=10\\\\√(36+(y+1)^2)=10\ \ \ |square\ both\ sides\\\\36+(y+1)^2=10^2\\\\36+(y+1)^2=100\ \ \ |subtract\ 36\ from\ both\ sides\\\\(y+1)^2=64\iff y+1=-√(64)\ or\ y+1=√(64)\\\\y+1=-8\ or\ y+1=8\ \ \ \ |subtract\ 1\ from\ both\ sides\\\\y=-9\ or\ y=7`


`Answer:{\boxed{(4;-9)\ or\ (4;\ 7)}`