Question

Trong mat phang voi he toa do Oxy, cho 2 diem A(3;1), B(-1;3) & duong thang d: 3x-y-2=0

Lap pt duong tron (C) co tam thuoc duong thang d & di qua 2 diem A, B

Answer 1

Gọi tâm I thuộc d : 3x-y-3=0 nên \(I\left(a;3a-2\right)\)Vì (C) đi qua A và B nên ta có IA=IB

\(\overrightarrow{IA}=\left(3-a;3-3a\right)\Rightarrow IA^2=\left(3-a\right)^2+\left(3-3a\right)^2\)

\(\overrightarrow{IB}=\left(-1-a;5-3a\right)\Rightarrow IB^2=\left(1+a\right)^2+\left(5-3a\right)^2\) 

Có IA=IB nên \(\left(3-a\right)^2+\left(3-3a\right)^2=\left(1+a\right)^2+\left(5-3a\right)^2\Leftrightarrow-8+4a=0\Leftrightarrow a=2\) Vậy I(2;4) \(R=IA=\sqrt{10}\)

Vậy ptdt (C) là : \(\left(x-2\right)^2+\left(y-4\right)^2=10\)