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 Aa n dB . Then find the locus of the midpoint of A Bdot

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

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.

If a tangent to the parabola y^2=4a x meets the x-axis at T and intersects the tangents at vertex A at P , and rectangle T A P Q is completed, then find the locus of point Qdot

From any point on the line y=x+4, tangents are drawn to the auxiliary circle of the ellipse x^2+4y^2=4 . If P and Q are the points of contact and Aa n dB are the corresponding points of Pa n dQ on he ellipse, respectively, then find the locus of the midpoint of A Bdot

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

If the ellipse x^2/a^2+y^2/b^2=1 (b > a) and the parabola y^2 = 4ax cut at right angles, then eccentricity of the ellipse is

If the chord of contact of tangents from a point P to the parabola y^2=4a x touches the parabola x^2=4b y , then find the locus of Pdot

If 4x+y+k=0 is a tangent to the ellipse x^(2)+3y^(2)=3 then k = ?

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