Answer to Question #256925 in Analytic Geometry for Snow

Question

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

Answer 1

Equations of lines are:

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

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

$y=-4,x=2$

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

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

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

Equation of circle is:

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