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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
The second part gives you a circle, just using circle equation knowledge, being %28x-5%29%5E2%2B%28y-3%29%5E2=25; 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: sqrt%28%28x-0%29%5E2%2B%28y-y%29%5E2%29=3, but not really necessary.
You know "3 units from the y-axis", so x=-3 or x=3. This can also be stated, x%5E2=9.

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,
%28y-3%29%5E2=-%28x-5%29%5E2%2B25
y-3=0%2B-+sqrt%2825-%28x-5%29%5E2%29
highlight%28y=3%2B-+sqrt%2825-%28x-5%29%5E2%29%29-------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 x=-3 will not work because the square root will become sqrt%2825-%28-3-5%29%5E2%29=sqrt%2825-64%29=sqrt%28-39%29, which is Complex, not Real. If you must have REAL number coordinates, then you can only choose x=3.