A circle of radius 4, is concentric with the elllipse `3x^2+13y^2=78`. Prove that a common tangent is inclined to the major axis at an angle `pi/4`

A circle of radius 4, is concentric with the ellipse 3x^(2) + 13y^(2) = 78 . Prove that a common tangent is inclined to the major axis at an angle (pi)/(4)

A circle of radius r is concentric with the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 Prove that slope of the common tangent of the above curves is sqrt((r^(2)-b^(2))/(a^(2)-r^(2)))

If a circle is concentric with the ellipse, find the in­clination of their common tangent to the major axis of the ellipse.

The equation of tangent to the ellipse 2x^(2)+3y^(2)=6 which make an angle 30^(@) with the major axis is

Show that the common tangent of the ellipse 3x^(2) +13y^(2) =78 and the circle x^(2) + y^(2) =16 is inclined at 45^(@) with the major axis.

Show that the curves x^(2)+y^(2)=2, 3x^(2)+y^(2)=4x have a common tangent at the point (1,1)

Find the equations of tangents to the ellipse 2x^2+y^2=8 which are which makes an angle pi/4 with x-axis.

The slope of a common tangent to the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 and a concentric circle of radius r is