If a tangent of slope 4 of the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` is normal to the circle `x^(2)+y^(2)+4x+1=0` then the maximum value of `ab` is

If a tangent of slope 2 of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is the normal to the circle x^(2)+y^(2)+4x+1=0 then the maximum value of a.b is equal to

If a tangent of slope 2 of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is normal to the circle x^(2)+y^(2)+4x+1=0, then the maximum value of ab is 4 (b) 2 (c) 1 (d) none of these

If a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with slope m is a normal to the circle x^(2)+y^(2)+4x+1=0, then the maximum value of ab is (A)2m(B)4m(C)m(D)6m

If a tangent of slope (1)/(3) of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a>b) is normal to the circle x^(2)+y^(2)+2x+2y+1=0 then

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

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

A tangent of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is normal to the hyperbola (x^(2))/(4)-(y^(2))/(1)=1 and it has equal intercepts with positive x and y axes, then the value of a^(2)+b^(2) is

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