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

[NormanJaden12]

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: https://imgur.com/a/0wAnqcU)

Homework Equations

Here's a link: https://imgur.com/a/y71Z9GY

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 (https://math.stackexchange.com/ques...ntre-of-circle-with-equation-of-tangent-given) 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.

 

[YoungPhysicist]

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.

 

[neilparker62]

You can get equations for 2 diameters out of the given information. Then solve simultaneously for the centre.