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

Jan 2, 2017

Points on the circle ${\left(x - 12\right)}^{2} + {y}^{2} = {13}^{2}$

#### 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, $\alpha = 12 , \beta = 0 \mathmr{and} a = 13$.

See the graph.

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