The points of intersection of the line ax + by = 0,(a ≠ b) and the circle x² + y² - 2x = 0 are A(α,0) and B(1,β). The image of the circle with AB as a diameter in the line x + y + 2 = 0 is:

(A) x² + y² + 5x + 5y + 12 = 0

(B) x² + y² + 3x + 5y + 8 = 0

(C) x² + y² - 5x - 5y + 12 = 0

(D) x² + y² + 3x + 3y + 4 = 0

Coordinate Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 25 Jan, Morning shift · Q3027

JEE Main 202325 Jan, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

The points of intersection of the line

ax + by = 0,(a \ne b)

and the circle

{x^2} + {y^2} - 2x = 0

are

A(\alpha ,0)

and

B(1,\beta )

. The image of the circle with AB as a diameter in the line

x + y + 2 = 0

is :