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Q.

Determine the equation of the circle which touches the line x-y= 0 at the origin and bisects the circumference of the circle.

x2 + y2 +2y-3=0

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a

x2 + y2 - 3y=0

b

x2 + y2 -5x +5y = 0

c

x2 + y2 + 5x -5y= 0

d

x2 + y2 + 3y - 3x= 0 

answer is B.

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Detailed Solution

The line x-y = 0 touches at (0,0)
S1 = x2 + y2 + λx-y 1= 0    ----(1)
S2 = x2 + y2 + 2y - 3 = 0 -----(2)
 S1 bisects the circumference of S2 .
Common chord S1 - S2 = 0 posses though the centre co, 1 of S2 ∴  λ(x-y) - 2y + 3= 0
 Λ + 2+ 3 = 0    =   λ= -5  put the equ (1)
x2 + y2 - 5x + 5y = 0
         Type -  CBSE
Class-  Grade 10
Topic-  Arithmetic Progression
 
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Determine the equation of the circle which touches the line x-y= 0 at the origin and bisects the circumference of the circle.x2 + y2 +2y-3=0