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

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

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

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

Tangent are drawn from the point (3, 2) to the ellipse x^2+4y^2=9 . Find the equation to their chord of contact and the middle point of this chord of contact.

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.

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.

A tangent is drawn at any point P(t) on the parabola y^(2)=8x and on it is takes a point Q(alpha,beta) from which a pair of tangent QA and OB are drawn to the circle x^(2)+y^(2)=8 . Using this information, answer the following questions : The locus of the point of concurrecy of the chord of contact AB of the circle x^(2)+y^(2)=8 is

A tangent is drawn at any point P(t) on the parabola y^(2)=8x and on it is takes a point Q(alpha,beta) from which a pair of tangent QA and OB are drawn to the circle x^(2)+y^(2)=8 . Using this information, answer the following questions : The locus of the point of concurrecy of the chord of contact AB of the circle x^(2)+y^(2)=8 is

From a point A common tangents are drawn to a circle x^2 +y^2 = a^2/2 and y^2 = 4ax . Find the area of the quadrilateral formed by common tangents, chord of contact of circle and chord of contact of parabola.

If y = mx is the equation of a chord of the circle x^2+y^2-2ax=0 with radius a, prove that the equation of the circle on this chord as a diameter is (1+m^2)(x^2+y^2)-2a(x + my)=0 .