The tangent at any point `P` on the circle `x^2+y^2=4` meets the coordinate axes at `Aa n dB` . Then find the locus of the midpoint of `A Bdot`

Consider an ellipse (x^2)/4+y^2=alpha(alpha is parameter >0) and a parabola y^2=8x . If a common tangent to the ellipse and the parabola meets the coordinate axes at Aa n dB , respectively, then find the locus of the midpoint of A Bdot

Consider the family ol circles x^2+y^2=r^2, 2 < r < 5 . If in the first quadrant, the common tangnet to a circle of this family and the ellipse 4x^2 +25y^2=100 meets the co-ordinate axes at A and B, then find the equation of the locus of the mid-point of AB.

The tangent at any point on the curve x=acos^3theta,y=asin^3theta meets the axes in Pa n dQ . Prove that the locus of the midpoint of P Q is a circle.

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

The tangents at any point P of the circle x^(2)+y^(2)=16 meets the tangents at a fixed point A at T. Point is joined to B, the other end of the diameter, through, A. The sum of focal distance of any point on the curce is

The tangent at P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ is

If a circle of constant radius 3k passes through the origin O and meets the coordinate axes at Aa n dB , then the locus of the centroud of triangle O A B is (a) x^2+y^2=(2k)^2 (b) x^2+y^2=(3k)^2 (c) x^2+y^2=(4k)^2 (d) x^2+y^2=(6k)^2

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 the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Qa n dR , then find the midpoint of chord Q Rdot

If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at Aa n dB , then find the locus of the point of intersection of the tangents at Aa n dBdot