Question

How do you find all points on the y-axis of a Cartesian coordinate system that are 13 units from the point (12,0)?

Answer 1

Points on the circle `(x-12)^2+y^2= 13^2`

Explanation:

The locus of (x, y) that is at the same distance a from #(alpha, beta)

is the circle

`(x-alpha)^2+y-beta)^2=a^2`

Here, `alpha = 12, beta = 0 and a = 13`.

See the graph.

graph{(x-12)^2+y^2-13^2=0 [-30.87, 30.88, -15.44, 15.43]}