Q:

How do I find all points on the y-axis that are a distance 6 from P(5,3)?

How do I solve this problem?
find all points on the y-axis that are a distance 6 from P(5,3)

A:

Another hint that may help, try drawing a picture. All the points that are a distance of 6 from the point P(5,3) is simply a circle with center P(5,3) and a radius of 6. If you can graph this circle, your next step would be to find the points of intersection with the y-axis. 

A:

Hint: Write the point on the $y$-axis as $(0, y)$ for some $y$. The distance equation then states that
$$6 = d\left((0, y), (5, 3)\right) = \sqrt{(0 - 5)^2 + (y - 3)^2} = \sqrt{25 + (y - 3)^2}$$
Now square both sides and solve.

