Find all points having a y- coordinate of -3 and whose distance from point (1,2) is 3

Question

and if possible there is one more equation like it if you could explain too...Find all points on the x-axis that are 5 units from the point (2, -30). Thank you. 

Answer 1

Let A = (x,-3) and B = (1,2)

 

If the distance from A to B is 3, then √ [(x-1)² + (-3-2)²] = 3

 

Square both sides to obtain x² - 2x + 17 = 0.  This equation has complex roots.

 

So, there aren't any points that meet the stated criteria.