Find the center of a circle given a tangent line & point

  • #1

Homework Statement

"Find the center and radius of the circle that passes through A(1,1) and is tangent to the line y=2x-3 at the point B(3,3). (Picture of the graph:

Homework Equations

Here's a link:

The Attempt at a Solution

Soo, I've been tryiing to use the equation shown in the link above, but i get an answer that i don't quite get. In the website where i found this ( it told me to use the coordinates where the tangent touches the circle.

I used the points (3,3) and substitute it with the x0 and the y0, and substitute the m and c with 2 and 3 respectively. When i simplify the equation, i get 15/3 for both x and y points, which will result to another (3,3). I might've missed something but the resulted coordinates isn't the center of the given circle.

Answers and Replies

  • #2
your c is -3

And I don't think that's the formula you need: That formula only consists of the point where the circle touches the tangent and the linear equation. What about A(1,1)? Although I can't fully understand the formula, but just knowing the tangent point and equation won't be enough to make a circle(you can actually but you will make a infinite amount of them since A(1,1) doesn't matters), you need to find a formula that somehow takes the A(1,1) into a count.
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  • #3
You can get equations for 2 diameters out of the given information. Then solve simultaneously for the centre.
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