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=
`√((x1-x2)^2+(y1-y2)^2)`
given
distance between (-6,5) and (-3,y) is 5
5=
`√((-6-(-3))^2+(5-y)^2)`
5=
`√((-6+3)^2+(5-y)^2)`
5=
`√((-3)^2+(5-y)^2)`
5=
`√(9+y^2-10t+25)`
5=
`√(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)