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`

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

The locus represented by x cos alpha + y sin alpha = 4 cuts the coordinate axes at A and B . Find the locus of the midpoint of AB . (alpha is a parameter)

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

A straight line through the point of intersection of the lines x+2y = 4 and 2x +y =4 meets the coordinates axes at A and B. The locus of the midpoint of AB is

A straight line through the point of intersection of the lines x + 2y = 4 and 2 x + y = 4 meets the coordinate axes at A and B .the locus of the midpoint of AB is _

Equation of a common tangent to the circle x^(2)+y^(2)-6x=0 and the parabola y^(2)=4x is

Consider the family of 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.

Find the equation of the common tangent to the circle x^(2)+y^(2)=8 and the parabola y^(2)=16x .

The normal to the parabola y^(2)=8x at the point (2, 4) meets the parabola again at the point-

Find the locus of the midpoint of normal chord of parabola y^2=4a xdot