A line touches the ellipse `(x^2)/(a^(2))+(y)/(b^(2))=1` and the circle `x^(2)+y^(2)=r^(2)` ,then the slope `m` of the common tangent is given by `m^(2)=`

A line touches the ellipse x 2 a 2 + y 2 b 2 = 1 and the circle x^(2)+y^(2)=r^(2) ,then the slope m of the common tangent is given by m^(2) =

If the line lx+my +n=0 touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then

If chord of contact of the tangent drawn from the point (a,b) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the circle x^(2)+y^(2)=k^(2), then find the locus of the point (a,b).

Ifchord ofcontact ofthe tangents drawn from the point (alpha,beta) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the circle x^(2)+y^(2)=c^(2), then the locus of the point

If the line y=x+c touches the ellipse 2x^(2)+3y^(2)=1 then c=

The equation of common tangents to the ellipse x^(2)+2y^(2)=1 and the circle x^(2)+y^(2)=(2)/(3) is

A straight line PQ touches the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 and the circle x^(2)+y^(2)=r^(2)(bltrlta) . RS is a focal chord of the ellipse. If RS is parallel to PQ and meets the circle at points R and S. Find the length of RS.

The number of common tangents to the ellipse (x^(2))/(16) + (y^(2))/(9) =1 and the circle x^(2) + y^(2) = 4 is

If a tangent having slope 2 of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is normal to the circle x^(2)+y^(2)+bx+1=0 , then the vlaue of 4a^(2)+b^(2) is equal to