Locus of the mid points of the chords of the circle `x^2+y^2=a^2` which pass through the fixed point `(h ,k)` is `x^2+y^2+2h x+2k y=0` `x^2+y^2-2h x-2k y=0` `x^2+y^2+h x+k y=0` `x^2+y^2-h x-k y=0` `x^2+y^2+h x-k y=0`

Show that the locus of the middle point of all chords of the parabola y^2 = 4ax passing through a fixed point (h, k) is y^2 - ky=2a(x-h) .

The locus of mid-points of the chords of the circle x^2 - 2x + y^2 - 2y + 1 = 0 which are of unit length is :

The locus of the mid-point of a chord of the circle x^2 + y^2 -2x - 2y - 23=0 , of length 8 units is : (A) x^2 + y^2 - x - y + 1 =0 (B) x^2 + y^2 - 2x - 2y - 7 = 0 (C) x^2 + y^2 - 2x - 2y + 1 = 0 (D) x^2 + y^2 + 2x + 2y + 5 = 0

Equation of the diameter of the circle x^2+y^2-2x+4y=0 which passes through the origin is a.x+2y=0 b.x-2y=0 c. 2x+y=0 d. 2x-y=0.

The locus of the centre of the circle passing through the intersection of the circles x^2+y^2= 1 and x^2 + y^2-2x+y=0 is

From the points (3, 4), chords are drawn to the circle x^2+y^2-4x=0 . The locus of the midpoints of the chords is (a) x^2+y^2-5x-4y+6=0 (b) x^2+y^2+5x-4y+6=0 (c) x^2+y^2-5x+4y+6=0 (d) x^2+y^2-5x-4y-6=0

The equation of the circle having its centre on the line x+2y-3=0 and passing through the points of intersection of the circles x^2+y^2-2x-4y+1=0a n dx^2+y^2-4x-2y+4=0 is x^2+y^2-6x+7=0 x^2+y^2-3y+4=0 c. x^2+y^2-2x-2y+1=0 x^2+y^2+2x-4y+4=0

The point of tangency of the circles x^2+ y^2 - 2x-4y = 0 and x^2 + y^2-8y -4 = 0 , is

The point of tangency of the circles x^2+ y^2 - 2x-4y = 0 and x^2 + y^2-8y -4 = 0 , is

The chords of contact of the pair of tangents drawn from each point on the line 2x + y=4 to the circle x^2 + y^2=1 pass through the point (h,k) then 4(h+k) is