Suppose is the equation of a circle such that has equal roots (each equal to 2) and…

MATHEMATICS · Single correct · AoPS · Mathematics · Graphing Quadratics · Graphing Quadratics

Problem

Suppose

f(x,y) = 0

is the equation of a circle such that

f(x,1) = 0

has equal roots (each equal to 2) and

f(1,x) = 0

also has equal roots (each equal to zero). The equation of circle is (1)

x^2 + y^2 + 4x + 3 = 0

(2)

x^2 + y^2 + 4y + 3 = 0

(3)

x^2 + y^2 + 4x - 3 = 0

(4)

x^2 + y^2 - 4x + 3 = 0