The locus of the centre of all circles passing through (2, 4) and cutting `x^2 + y^2 = 1` orthogonally is : (A) `4x+8y = 11` (B) `4x+8y=21` (C) `8x+4y=21` (D) `4x-8y=21`

The locus of the centre of the circle passing through (1,1) and cutting x^2 + y^2 = 4 orthogonally is : (A) x+y=3 (B) x+2y=3 (C) 2x+y=3 (D) 2x-y=3

The locus of the centre of the circle cutting the circles x^2+y^2–2x-6y+1=0, x^2 + y^2 - 4x - 10y + 5 = 0 orthogonally is

The least length of chord passing through (2,1) of the circle x^(2)+y^(2)-2x-4y-13=0 is

Find the locus of the centre of the circle which cut the circles x^2+y^2+4x-6y+9=0 and x^2+y^2-4x+6y+4=0 orthogonally (a) 9x+10y-7=0 (b) 8x-12y+5=0 (c) 9x-10y+11=0 (d) 9x+10y+7=0

If a circle passes through (1,2) and cuts x^2+y^2=4 orthogonally then show that the equation of the locus of centre is 2x+4y-9=0

Show that x^2+4y^2=8 and x^2-2y^2=4 intersect orthogonally

The equation of the circle passing through (1/2, -1) and having pair of straight lines x^2 - y^2 + 3x + y + 2 = 0 as its two diameters is : (A) 4x^2 + 4y^2 + 12x - 4y - 15 = 0 (B) 4x^2 + 4y^2 + 15x + 4y - 12 = 0 (C) 4x^2 + 4y^2 - 4x + 8y + 5 = 0 (D) none of these

Find the center of the smallest circle which cuts circles x^2+y^2=1 and x^2+y^2+8x+8y-33=0 orthogonally.

The equation of circle passing through (1,-3) and the points common to the two circt x^2 + y^2 - 6x + 8y - 16 = 0, x^2 + y^2 + 4x - 2y - 8 = 0 is

Let P be the point on the parabola, y^2=8x which is at a minimum distance from the centre C of the circle, x^2+(y+6)^2=1. Then the equation of the circle, passing through C and having its centre at P is : (1) x^2+y^2-4x+8y+12=0 (2) x^2+y^2-x+4y-12=0 (3) x^2+y^2-x/4+2y-24=0 (4) x^2+y^2-4x+9y+18=0