Consider the circles and and the line

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Consider the circles

C_1 \equiv x^2 + y^2 - 2x - 4y - 4 = 0

and

C_2 \equiv x^2 + y^2 + 2x + 4y + 4 = 0

and the line

L \equiv x + 2y + 2 = 0

, then (1)

L

is the radical axis of

C_1

and

C_2

(2)

L

is the common tangent of

C_1

and

C_2

(3)

L

is the common chord of

C_1

and

C_2

(4)

L

is perpendicular to the line joining centres of

C_1

and

C_2