Question

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

Answer 1

`d=√((x_2-x_1)^2+(y_2-y_1)^2)\\\\ 10=√((4-(-2))^2+(y-(-1))^2)\\ 10=√(6^2+(y+1)^2)\\ 10=√(36+y^2+2y+1)\\ 10=√(y^2+2y+37)\\ 100=y^2+2y+37\\ y^2+2y-63=0\\ y^2+9y-7y-63=0\\ y(y+9)-7(y+9)=0\\ (y-7)(y+9)=0\\ y=7 \vee y=-9\\\\ \boxed{(x,y)=\{(4,-9),(4,7)\}}`