Question

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

Answer 1

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