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)`=

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)=

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.

If the ellipse x^2/a^2+y^2/b^2=1 and the circle x^2+y^2=r^2 where bltrlta intersect in four points and the slope of a common tangent to the ellipse and the circle is b/a , then r^2 is equal to

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).

Slope of tangent to the circle (x-r)^(2)+y^(2)=r^(2) at the point (x.y) lying on the circle is

A straight line x=y+2 touches the circle 4(x^(2)+y^(2))=r^(2), The value of r is:

Find the common tangents to the hyperbola x^(2)-2y^(2)=4 and the circle x^(2)+y^(2)=1