# Thread: All Points On (0, y)

1. ## All Points On (0, y)

Find all the points on the y-axis aka (0, y) that are 6 units from the point (4, -3).

Seeking the steps to solve on my own.

2. ## Re: All Points On (0, y)

Originally Posted by harpazo
Find all the points on the y-axis aka (0, y) that are 6 units from the point (4, -3).
Seeking the steps to solve on my own.
Solve $\sqrt{(4-0)^2+(-3-y)^2}=6$

3. ## Re: All Points On (0, y)

Originally Posted by harpazo
Find all the points on the y-axis aka (0, y) that are 6 units from the point (4, -3).

Seeking the steps to solve on my own.
Have you drawn a diagram?

4. ## Re: All Points On (0, y)

Geometrically, open compasses to a distance 6 between the points. Set one point at (4, -3) and strike an arc of radius 6. The two points where that arc crosses the y-axis are the desired point. Of course, such an arc is a circle of radius 6 with center at (4, -3) which has equation $\displaystyle (x- 4)^2+ (y+ 3)^2= 36$. A point on the y-axis has x= 0 so the equation becomes $\displaystyle 16+ (y+ 3)^2= 36$. Then $\displaystyle (y- 3)^2= 36- 60= 20$. $\displaystyle y- 3= \pm\sqrt{20}= \pm 2\sqrt{5}$ and $\displaystyle y= 3\pm 2\sqrt{5}$.

5. ## Re: All Points On (0, y)

Originally Posted by Plato
Solve $\sqrt{(4-0)^2+(-3-y)^2}=6$
I can take it from here.