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.

From the variable point A on circle x^2+y^2=2a^2, two tangents are drawn to the circle x^2+y^2=a^2 which meet the curve at Ba n dCdot Find the locus of the circumcenter of A B Cdot

If the intercepts of the variable circle on the x- and yl-axis are 2 units and 4 units, respectively, then find the locus of the center of the variable circle.

Find the equation of the chord of the circle x^2+y^2=a^2 passing through the point (2, 3) farthest from the center.

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

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 any point on any directrix of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,a > b , a pari of tangents is drawn to the auxiliary circle. Show that the chord of contact will pass through the correspoinding focus of the ellipse.

A variable circle passes through the point A(a ,b) and touches the x-axis. Show that the locus of the other end of the diameter through A is (x-a)^2=4b y .

From a point P on the normal y=x+c of the circle x^2+y^2-2x-4y+5-lambda^2-0, two tangents are drawn to the same circle touching it at point Ba n dC . If the area of quadrilateral O B P C (where O is the center of the circle) is 36 sq. units, find the possible values of lambdadot It is given that point P is at distance |lambda|(sqrt(2)-1) from the circle.

A circle passes through (0,0) and (1, 0) and touches the circle x^2 + y^2 = 9 then the centre of circle is -

If the tangents are drawn to the circle x^2+y^2=12 at the point where it meets the circle x^2+y^2-5x+3y-2=0, then find the point of intersection of these tangents.