SOLUTION: Question: Find an equation for a circle with center ( ―2, 3), tangent (touching at one point) to the y-axis. My Attempt: Formula for a circle: (x-h)^2+(y-k)^2=r^2 (x+2)^2+(

Algebra ->  Graphs -> SOLUTION: Question: Find an equation for a circle with center ( ―2, 3), tangent (touching at one point) to the y-axis. My Attempt: Formula for a circle: (x-h)^2+(y-k)^2=r^2 (x+2)^2+(      Log On


   

Question 1206417: Question: Find an equation for a circle with center ( ―2, 3), tangent (touching at one point) to the y-axis.
My Attempt:
Formula for a circle: (x-h)^2+(y-k)^2=r^2
(x+2)^2+(y-3)^2=r^2
Would this be the final equation? And if I am given a specific point that passes through the y-axis I would substitute that given ordered pair into x and y and solve for r^2, then replace it back into the original equation correct?
For example: Center = (-2,3) passes through (3,7)
(3+2)^2+(7-3)^2=r^2
sqrt(41)=r
Final equation = (x+2)^2+(y-3)^2=sqrt(41)
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

Formula for a circle:
%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2.....center ( -2, 3)
The circle is tangent to the y-axis (we know that tangent refers to a line that touches something at exactly one point, we want the circle to have a radius that will make it just big enough to reach the y-axis), hence its radius r=x-coordinate=-2
%28x%2B2%29%5E2%2B%28y-3%29%5E2=%28-2%29%5E2
%28x%2B2%29%5E2%2B%28y-3%29%5E2=4







Answer by ikleyn(53751) About Me  (Show Source):
You can put this solution on YOUR website!
.

The problem contains a tip to you to determine the radius.

Since the center is the point  (-2,3),  from it you  IMMEDIATELY conclude that
the radius of the circle is  2  units,  since the circle touches  y-axis.

As soon as you know the center and the radius,  the rest is just obvious.

The final equation of the circle is

        %28x%2B2%29%5E2 + %28y-3%29%5E2 = 2%5E2,

or,  which is the same

        %28x%2B2%29%5E2 + %28y-3%29%5E2 = 4.

===============

Solved.

Never say that the radius is -2, as the other person does.

A radius of a circle  (of any circle)  is always a positive value
and can not be negative.


\\\\\\\\\\\\\\\\\\\\\


You ask in your post, if your logic works.

No, the logic presented in your post does not work in this problem.

It does not work, because you try to use some info, which is not given in the problem,
and try to make conclusions from false/irrelevant premises.