Q: If a rectangular hyperbola (x – 1)(y – 2) = 4 cuts a circle x^{2} + y^{2} + 2gx + 2fy +c = 0 at points (3, 4), (5, 3), (2, 6) and (-1, 0), then the value of (g + f) is equal to

(A) 8

(B) -9

(C) -8

(D) 9

Sol. Let x_{i}y_{i}, i = 1, 2, 3, 4 be the points of intersection of hyperbola and circle, then

$\Large \frac{\Sigma x_i}{4} = \frac{-g+1}{2} $

g = -7/2

and $\Large \frac{\Sigma y_i}{4} = \frac{-f+1}{2} $

∴ f = -9/2

g + f = -8.

Hence (C) is the correct answer.

#### Also Read :

- The circle described on the line joining the points (0, 1), (a, b) as diameter cuts the…
- If the line y – mx + m – 1 = 0 cuts the circle x^2 + y^2 – 4x – 4y + 4 = 0 at two real…
- The straight line y = mx + c cuts the circle x^2 + y^2 = a^2 at real points if
- The centre of the circle S = 0 lies on the line 2x - 2y + 9 = 0 and S = 0 cuts orthogonally…
- The equation of a line passing through the centre of a rectangular hyperbola is x – y – 1 =…
- The locus of the centre of a circle which passes through the origin and cuts off a length 2b…
- The locus of the middle points of chords of hyperbola 3x^2 – 2y^2 + 4x – 6y = 0 parallel to…
- The centre of a circle passing through the points (0, 0) , (1, 0) and touching the circle…
- If tangents be drawn to the circle x^2 + y^2 = 12 at its points of intersection, with the…
- If (mi , 1/mi) i = 1, 2, 3, 4 mi > 0 are 4 distinct points on a circle, then show that m1…