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

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

Determine the locus of the mid-points of equals chords of a circle .

Tangents are drawn to the ellipse x^2+2y^2=2 , then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

If the line hx+ky=1 touches x^2+y^2=a^2 , then the locus of the point (h,k) is a circle of radius

Let A B be chord of contact of the point (5,-5) w.r.t the circle x^2+y^2=5 . Then find the locus of the orthocentre of the triangle P A B , where P is any point moving on the circle.

The normal to-be circle x^2 +y^2 - 4x + 6y -12=0 passes through the point

A variable chord is drawn through the origin to the circle x^2+y^2-2a x=0 . Find the locus of the center of the circle drawn on this chord as diameter.

If a circle passes through the point (a,b) and cuts the circle x ^(2) +y^(2) =p^(2) orthogonally, then the equation of the locus of its centre is-

From an arbitrary point P on the circle x^2+y^2=9 , tangents are drawn to the circle x^2+y^2=1 , which meet x^2+y^2=9 at A and B . The locus of the point of intersection of tangents at A and B to the circle x^2+y^2=9 is (a) x^2+y^2=((27)/7)^2 (b) x^2-y^2((27)/7)^2 (c) y^2-x^2=((27)/7)^2 (d) none of these

The centres of a set of circles, each of radius 3 , lie on the circle x^2+y^2=25 . The locus of any point in the set is