Question

Find all points having an x coordinate of -3 whose distance from the point (-6,5) is 5

Answer 1

Ok
distance formula

D=$\sqrt{(x1-x2)^2+(y1-y2)^2}$
given
distance between (-6,5) and (-3,y) is 5
5=$\sqrt{(-6-(-3))^2+(5-y)^2}$
5=$\sqrt{(-6+3)^2+(5-y)^2}$
5=$\sqrt{(-3)^2+(5-y)^2}$
5=$\sqrt{9+y^2-10t+25}$
5=$\sqrt{y^2-10t+34}$
square both sides
25= $y^2-10t+34$
minus 25 both sides
$0= y^2-10t+9$
factor
0=(y-9)(y-1)
set to zero
0=y-9
9=y

0=y-1
1=y

the points are (-3,1) and (-3,9)