Question

Find the equation of the circle which passes
through the point of intersection of the lines
3x-2y-1 = 0 and 4x+ y - 27=0 and whose centre is (2,-3).​

Answer 1

The point of intersection is the solution of system of equation $\left \{ {{3x-2y-1=0} \atop {4x+y-27=0}} \right.$ .

The point of intersection is $(5,7)$.

The centre of the circle is $(2,-3)$.

Let the radius of the circle be $r$.

Then $r^2=3^2+10^2=109$.

the equation

∴ $(x-2)^2+(y+3)=109$

(+ Attatchment)