The number of normals to the ellipse `x^2/25+y^2/16= 1` which are tangents to the circle `x^2+y^2 = 9` is

The auxiliary circle of the ellipse x^(2)/25 + y^(2)/16 = 1

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

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

The locus of the mid-points of the chords of the circle x^(2) + y^(2) = 16 which are the tangents to the hyperbola 9x^(2) - 16y^(2) = 144 is

The line x-y + k =0 is normal to the ellipse (x^2)/(9) + (y^2)/(16)=1 , then k=

If the tangent to the ellipse x^2 +4y^2=16 at the point is normal to the circle x^2 +y^2-8x-4y=0 then theta is equal to

If the tangent to the ellipse x^2 +4y^2=16 at the point theta normal to the circle x^2 +y^2-8x-4y=0 then theta is equal to

The locus of mid-point of the chord of circle x^2+y^2=16 , which are tangent to the hyperbola 9x^2-16y^2=144 , is