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`

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)+2hx+2ky=0x^(2)+y^(2)-2hx-2ky=0x^(2)+y^(2)+hx+ky=0x^(2)+y^(2)-hx-ky=0x^(2)+y^(2)+hx-ky=0

The locus of the mid-point of the chords of the circle x^(2)+y^(2)-4x-6y-3=0 which subtend a right angle at the point(h,k),is

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 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

If the radius of the circle x^(2)+y^(2)-18x+12y+k=0 be 11, then k=

If the locus of the mid points of the chords of the circle x^(2)+y^(2)-2x+2y-2=0 which are parallel to the line y=x+5 is ax+by+c=0(a>0) then (a+c)/(b)=

If the gradient one of the lines x^2+h x y+2y^2=0 is twice that of the other, then h=_______

Show that the circle through three points the normals at which to the parabola y^(2)=4ax are concurrent at the point (h,k) is 2(x^(2)+y^(2))-2(h+2a)x-ky=0

The equation of the curve,slope of whose tangent at any point (h,k) is (2k)/(h) and which passes through the point (1,1) is (i)x^(2)=y( ii) y^(2)=x( iii) x^(2)=2y( iv )y^(2)=2x

Through a fixed point (h,k), secant are drawn to the circle x^(2)+y^(2)=r^(2) . Show that the locus of the midpoints of the secants by the circle is x^(2)+y^(2)=hx+ky .