Show that locus of middle point of the portion of a tangent to the ellipse `x^2/a^2+y^2/b^2=1` inclined between the axes is `a^2/x^2+b^2/y^2=4`

The equation of the locus of the middle point of the portion of a tangent to the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 included between the axes is

The locus of the mid point of the portion of a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 included between the coordinate axes is

The locus of the middle points of portions of the tangents to the circle x^(2)+y^(2)=a^(2) terminated by the axes is

The locus of the point of intersection of the perpendicular tangents to the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 is

Find the locus of point of intersection of tangents to the ellipse x^2/a^2+y^2/b^2=1 which are inclined at an angle alpha with each other.

The locus of the point of intersection of the perpendicular tangents to the ellipse 2x^(2)+3y^(2)=6 is

If any tangent to the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 intercepts equal length l on the axes then l =