Question

Show that the equation of the circle passing through (1, 1) and the points of intersection of the circles `x^2+y^2+13 x-13 y=0` and `2x^2+2y^2+4x-7y-25=0` is `4x^2+4y^2+30 x-13 y-25=0.`
A. `4x^(2)+4y^(2)-30x-10y=25`
B. `4x^(2)+4y^(2)+30x-13y-25=0`
C. `4x^(2)+4y^(2)+17x-10y-25=0`
D. None of the above

Answer 1

Correct Answer - B
The required equation of circle is
`(x^(2)+y^(2)+13x-3y)+lambda(11x+(1)/(2)y+(25)/(2))=0" "...(i)`
Its passing through (1, 1),
`rArr 12 + lambda(24)=0`
`rArr lambda = (1)/(2)`
On putting in Eq. (i) , we get
`x^(2)+y^(2)+13x-3y-(11)/(2)x-(1)/(4)y-(25)/(4)=0`
`rArr 4x^(2)+4y^(2)+52x-12y-22x-y-25=0`
`rArr 4x^(2)+4y^(2)+30x-13y-25=0`