[" The common tangent of the ellipse "(x^(2))/(a^(2))+(y^(2))/(b^(2))-(2x)/(c)=0" and "(x^(2))/(b^(2))+],[" origin,then "theta=?]

Prove that the common tangent of the ellipses (x^(2))/(a^(2))+(y^(2))/(b^(2))-(2x)/(c)=0 and (x^(2))/(b^(2))+(y^(2))/(a^(2))-(2x)/(c)=0 subtends a right angle at the origin.

The condition that y=m x+c is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 is

Slope of the common tangent to the ellipse (x^(2))/(a^(2)+b^(2))+(y^(2))/(b^(2))=1,(x^(2))/(a^(2))+(y^(2))/(a^(2)+b^(2))=1 is

which one of the following is the common tangent to the ellipses,(x^(2))/(a^(2)+b^(2))+(y^(2))/(b^(2))=1 and (x^(2))/(a^(2))+(y^(2))/(a^(2)+b^(2))=1?

Length of common tangents to the hyperbolas (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and (y^(2))/(a^(2))-(x^(2))/(b^(2))=1 is

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

If y=m x+c is a tangent to (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 then b^(2) =

The number of common tangents to the circles x^(2)+y^(2)=0, x^(2)+y^(2)+x=0 is

If y=mx+c is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then the point of contact is