SOLUTION: What are the coordinates of the point 3 units from the y-axis and at a distance sqrt. of 5 from (5,3)?

Question 815686: What are the coordinates of the point 3 units from the y-axis and at a distance sqrt. of 5 from (5,3)?
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
The second part gives you a circle, just using circle equation knowledge, being ; the first part, depends how clever you are. You can use distance formula to develop an equation for it....

Three units from y-axis or from a general point (0,y).
Distance Formula: , but not really necessary.
You know "3 units from the y-axis", so or . This can also be stated, .

This plan is now to solve the circle for y, treating x as a constant.
Then, solve for y using separately x=-3 and for x=3. I believe these will be two solutions *, two points. To get started,

-------partway toward solution.
.
at which extent you can now use both values for x and compute the corresponding values for y.

*Note that this has ONE Real solution. The choice of will not work because the square root will become , which is Complex, not Real. If you must have REAL number coordinates, then you can only choose .
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