SOLUTION: The circle with equation x�+y�-4x-6y+9=0 touches the y-axis. Find (a) the coordinates of the point of contact. (b) the length of the tangent to the circle from the origin.

Question 1107302: The circle with equation
x�+y�-4x-6y+9=0 touches the y-axis.
Find
(a) the coordinates of the point of contact.
(b) the length of the tangent to the circle from the origin.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
rewrite as x^2-4x+y^2-6y=-9
complete the square for x and y
x^2-4x+4+y^2-6y+9=-9+13
(x-2)^2+(y-3)^2=4
This is a circle with center (2, 3) and radius 2
It touches the y-axis where x=0
Therefore, (-2)^2+(y-3)^2=4
(y-3)^2=0
y=3, so it touches at (0,3) and is a "bounce," 3 units from the origin.

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