Question #256925

Find the equation of a circle with center at (-1,-3) passing through the intersection point of the two lines: 4x+y-4=0 and x-y-6=0


1
Expert's answer
2021-10-28T11:50:56-0400

Equations of lines are:

4x+y4=0(1)xy6=0(2)4x+y-4=0\ldots(1)\\ x-y-6=0\ldots(2)

From (1)(1) and (2)(2), we get:

y=4,x=2y=-4,x=2

\therefore Point of intersection is (2,4).(2,-4).

Now, center of circle is (1,3).(-1,-3).

\therefore Radius is (2+1)2+(4+3)2=10\sqrt{(2+1)^2+(-4+3)^2}=\sqrt{10}

Equation of circle is:

(x+1)2+(y+3)2=10x2+y2+2x+6y=0(x+1)^2+(y+3)^2=10\\ \Rightarrow x^2+y^2+2x+6y=0


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