Question

Find all points (x,y) that are 13 units away from the point (2,7) and that lie on the line x - 2y = 10. Give your answer as a list of points separated by semicolons, with the points ordered such that their x-coordinates are in increasing order. So "(1,-3); (2,3); (5,-7)" - without the quotes - is a valid answer format.)

Answer 1

all points (x,y) that are 13 units away from the point (2,7) defines a circle:

(x-2)^2 + (y-7)^2 = 169

so, the line x-2y=10 may intersect the circle in 0,1, or 2 points.

So, plug x=2y+10 into the equation of the circle and see where the two graphs intersect.

Answer 2

see whether you get what wolframalpha does:

https://www.wolframalpha.com/input/?i=solve+%28x-2%29^2+%2B+%28y-7%29^2+%3D+169,+x-2y%3D10