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 is circle with 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.

Tangents are drawn from any point on the hyperbola (x^2)/9-(y^2)/4=1 to the circle x^2+y^2=9 . Find the locus of the midpoint of the chord of contact.

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

A line is drawn through a fix point P( alpha, beta ) to cut the circle x^2 + y^2 = r^2 at A and B. Then PA.PB is equal to :

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.

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 Aa n dB . The locus of the point of intersection of tangents at Aa n dB to the circle x^2+y^2=9 is x^2+y^2=((27)/7)^2 (b) x^2-y^2((27)/7)^2 y^2-x^2=((27)/7)^2 (d) none of these

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

From a point on the circle x^2+y^2=a^2 , two tangents are drawn to the circle x^2+y^2=b^2(a > b) . If the chord of contact touches a variable circle passing through origin, show that the locus of the center of the variable circle is always a parabola.

consider a family of circles passing through two fixed points S(3,7) and B(6,5) . If the common chords of the circle x^(2)+y^(2)-4x-6y-3=0 and the members of the family of circles pass through a fixed point (a,b), then