Question

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

so far i have
5=sqrt((-1-2)^2+(-2-y)^2)
5=(-3)^2

how do i simplify the rest of the equation so i can find x. do i foil it out? thanks.

Answer 1

Geometrically, you are looking for the intersection of a vertical line (x=2) with a circle centred at (-1,-5) with a radius of 5.

Line L1: x=2
Circle C1: (x-(-1))²+(y-(-5))²=5²
(x+1)²+(y+5)²=25
Substitute x=2 in C1:
(2+1)²+(y+5)²=25
(y+5)²=25-3²=16=4²
(y+5) = ±4
So there are two solutions, y=-9 or y=-1

Answer 2

thank you!!

Answer 3

You're welcome.
Do give a check on the distance between the centre and the intersection points to complete the question.