Question

Find the equation of the circle having (1, -2) as its centre and passing through the intersection of the lines 3x + y = 14, and 2x + 5y = 18.

Answer 1

Intersection of $3x+y=14$ and $2x+5y=1$ is
Obtained by solving two equations.
x = 4 and y = 2
Point (4, 2) is on circle, hence it's distance from centre (1, -2) = Radius
$=\sqrt{(1-4{)}^2+(-2-2{)}^2}=\sqrt{9+16}=5$
Equation of the circle with centre (4, 2) and radius 5 is,
$(x-1{)}^2+(y+2{)}^2=2522-2x+1+y^2+4y+4=25x^2+y^2-2x+4y-20=0$