Question

The equation of the circle which passes through the points of intersection of the circles `x^(2)+y^(2)-6x=0` and `x^(2)+y^(2)-6y=0` and has its centre at (3/2, 3/2), is
A. `x^(2)+y^(2)+3x+3y+9=0`
B. `x^(2)+y^(2)+3x+3y=0`
C. `x^(2)+y^(2)-3x-3y=0`
D. `x^(2)+y^(2)-3x-3y+9=0`

Answer 1

Correct Answer - C
The equation of the required circle is
`x^(2)+y^(2)-6x+lambda (6x-6y)=0` [Using : `S_(1)+lambda(S_(2)-S_(1))=0`]
or, `x^(2)+y^(2)+6(lambda-1)x-6lambda y = 0 ` ...(i)
It has its centre at (3/2, 3/2)
`:. -3 (lambda-1)=(3)/(2) and 3 lambda = (3)/(2) rArr lambda = (1)/(2)`
Putting `lambda=(1)/(2)` in (i), we get `x^(2)+y^(2)-3x-3y=0`