Show that the minimum value of the length of a tangent to the ellipse `b^(2)x^(2)+a^(2)y^(2)=a^(2)b^(2)` intercepted between the axes is (a+b).

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

Show that the tangents at the end of any focal chord of the ellipse x^(2)b^(2)+y^(2)a^(2)=a^(2)b^(2) intersect on the directrix.

Show that the lenght of the portion of the tangent to the curve x^(2/3)+y^(2/3)=a^(2/3) at any point of it, intercept between the coordinate axes is contant.

The slop of the tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 at the point (a cos theta, b sin theta) - is

Show that the length of the portion of the tangent to the curve x^((2)/(3))+y^((2)/(3))=4 at any point on it, intercepted between the coordinate axis in constant.

Find the equation of the tangent to the ellipse x^2/a^2+y^2/b^2=1 at (x= 1,y= 1) .

Find the slope of normal to the ellipse , (x^(2))/(a^(2))+(y^(2))/(b^(2))=2 at the point (a,b).

The sum of the squares of the perpendiculars on any tangents to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 from two points on the minor axis each at a distance a e from the center is (a) 2a^2 (b) 2b^2 (c) a^2+b^2 (d) a^2-b^2

Find the slope of a common tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and a concentric circle of radius rdot