Through a fixed point (h, k) secants are drawn to the circle `x^2 +y^2 = r^2`. Then the locus of the mid-points of the secants by the circle is

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 .

Through a fixed point (h, k) secants are drawn to the circle x^(2) + y^(2) =a^(2) . The locus of the mid points of the secants intercepted by the given circle is

From (3,4) chords are drawn to the circle x^(2)+y^(2)-4x=0. The locus of the mid points of the chords is :

From the origin,chords are drawn to the circle (x-1)^(2)+y^(2)=1. The equation of the locus of the mid-points of these chords is circle with radius

From points on the circle x^2+y^2=a^2 tangents are drawn to the hyperbola x^2-y^2=a^2 . Then, the locus of mid-points of the chord of contact of tangents is:

From points on the straight line 3x-4y+12=0, tangents are drawn to the circle x^(2)+y^(2)=4. Then,the chords of contact pass through a fixed point.The slope of the chord of the circle having this fixed point as its mid- point is

If a circle Passes through point (1,2) and orthogonally cuts the circle x^(2)+y^(2)=4, Then the locus of the center is:

If a circle Passes through a point (1,2) and cut the circle x^(2)+y^(2)=4 orthogonally,Then the locus of its centre is