if a variable tangent of the circle `x^2+y^2=1` intersects the ellipse `x^2 + 2y^2 = 4` at `P ` and `Q.` then the locus of the points of intersection of the tangents at `P` and `Q` is

A variable tangent to the circle x^(2)+y^(2)=1 intersects the ellipse (x^(2))/(4)+(y^(2))/(2)=1 at point P and Q. The lous of the point of the intersection of tangents to the ellipse at P and Q is another ellipse. Then find its eccentricity.

A variable tangent to the circle x^(2)+y^(2)=1 intersects the ellipse (x^(2))/(4)+(y^(2))/(2)=1 at point P and Q. The lous of the point of the intersection of tangents to the ellipse at P and Q is another ellipse. Then find its eccentricity.

If normal of circle x^(2)+y^(2)+6x+8y+9=0 intersect the parabola y^(2)=4x at P and Q then find the locus of point of intersection of tangent's at P and Q.

If a tangent to the parabola y^2 = 4ax intersects the x^2/a^2+y^2/b^2= 1 at A and B , then the locus of the point of intersection of tangents at A and B to the ellipse is

If a tangent to the parabola y^2 = 4ax intersects the x^2/a^2+y^2/b^2= 1 at A and B , then the locus of the point of intersection of tangents at A and B to the ellipse is

If a tangent to the circle x^(2)+y^(2)=1 intersects the coordinate axes at distinct point P and Q. then the locus of the mid- point of PQ is

If 3x+4y=12 intersect the ellipse x^2/25+y^2/16=1 at P and Q , then point of intersection of tangents at P and Q.

If 3x+4y=12 intersect the ellipse (x^(2))/(25)+(y^(2))/(16)=1 at P and Q, then point of intersection of tangents at P and Q.

If a tangent to the circle x^(2)+y^(2)=1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is :

If a tangent to the circle x^(2)+y^(2)=1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is :