Question

Tangents `OP` and `OQ` are drawn from the origin o to the circle `x^2 + y^2 + 2gx + 2fy+c=0.` Find the equation of the circumcircle of the triangle `OPQ`.
A. `x^(2)+y^(2)+2gx+2fy=0`
B. `x^(2)+y^(2)+gx+fy=0`
C. `x^(2)+y^(2)-gx-fy=0`
D. `x^(2)+y^(2)-2gx-2fy=0`

Answer 1

Correct Answer - B
The equation of the chord of contact of tangents drawn from the origin to the circle
`x^(2)+y^(2)+2gx+2fy+c=0 is gx + fy + c=0` ...(i)
The equation circle passes through the intersection of the given circle and line (i). Therefore, its equation is
`(x^(2)+y^(2)+2gx+2fy+c)+lambda(g x + fy + c ) =0` ...(ii)
This passes through (0, 0).
`:. c +lambda c= 0 rArr lambda = -`
Putting `lambda=-1` in (ii), the equation of the required circle is
`x^(2)+y^(2)+gx+fy=0`