Question

Find all points having an x-coordinate of 2 whose distance from the point (-1,-2) is 5

Answer 1

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\ 5=\sqrt{(-1-2)^2+(-2-y_1)^2}\\ \sqrt{9+4+4y_1+y_1^2}=5\\ y_1^2+4y_1+13=25\\ y_1^2+4y_1-12=0\\ y_1^2+6y_1-2y_1-12=0\\ y_1(y_1+6)-2(y_1+6)=0\\ (y_1-2)(y_1+6)=0\\ y_1=2 \vee y_1=-6\\\\ \boxed{(2,2),(-6,2)}$