The points of intersection of the line a x+b y=0,(a ≠ b) and the circle x2+y2-2 x=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 :

Question

The points of intersection of the line a x+b y=0,(a ≠ b) and the circle x2+y2-2 x=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+3 x+3 y+4=0 (B) x2+y2+5 x+5 y+12=0 (C) x2+y2+3 x+5 y+8=0 (D) x2+y2-5 x-5 y+12=0

Tardigrade Admin · Accepted Answer

Only possibility α=0, β=1 ∴ equation of circle x 2+ y 2- x - y =0 Image of circle in x+y+2=0 is x2+y2+5 x+5 y+12=0

Q. The points of intersection of the line $a x + b y = 0, (a \neq = b)$ and the circle $x^{2} + y^{2} - 2 x = 0$ are $A (α, 0)$ and $B (1, β)$ . The image of the circle with $A B$ as a diameter in the line $x + y + 2 = 0$ is :

$x^{2} + y^{2} + 3 x + 3 y + 4 = 0$

$x^{2} + y^{2} + 5 x + 5 y + 12 = 0$

$x^{2} + y^{2} + 3 x + 5 y + 8 = 0$

$x^{2} + y^{2} - 5 x - 5 y + 12 = 0$

Only possibility $α = 0, β = 1$
$∴$ equation of circle $x^{2} + y^{2} - x - y = 0$
Image of circle in $x + y + 2 = 0$ is
$x^{2} + y^{2} + 5 x + 5 y + 12 = 0$

Q. 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 :

x2+y2+3x+3y+4=0

x2+y2+5x+5y+12=0

x2+y2+3x+5y+8=0

x2+y2−5x−5y+12=0