How many tangents to the circle `x^2 + y^2 = 3` are normal tothe ellipse `x^2/9+y^2/4=1?`

Let m be slope of a common tangent to the circle x^2+y^2 = 4 and the ellipse x^2/6+y^2/3=1 , then m^2 equals ( sqrt2 =1.41 )

If y = x + c is a normal to the ellipse x^2/9+y^2/4=1 , then c^2 is equal to

If tangents are drawn from any point on the circle x^(2) + y^(2) = 25 the ellipse (x^(2))/(16) + (y^(2))/(9) =1 then the angle between the tangents is

Find the equation of tangent to the ellipse 3x^2+y^2+2y=0 which are perpendiculor to the line 4x-2y=1 .

if a variable tangent of the circle x^(2)+y^(2)=1 intersects the ellipse x^(2)+2y^(2)=4 at P and Q. then the locus of the points of intersection of the tangents at P and Q is

Let theta be the acute angle between the tangents to the ellipse x^2/9 + y^2/1 = 1 and the circle x^2 + y^2 = 3 at their point of intersection in the first quadrat. Then tantheta is equal to :

Let theta be the acute angle between the tangents to the ellipse x^2/9 + y^2/1 = 1 and the circle x^2 + y^2 = 3 at their point of intersection in the first quadrat. Then tantheta is equal to :

Let a line L_(1) with slope 1 is a normal to the circle x^(2)+y^(2)+6y+2=0 and tangent to the ellipse " (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , then maximum value of area of ellipse (in square units),is