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 the common tangent is inclined to the major axis at an angle tan^(-1) sqrt((r^2-b^2)/(a^2 - r^2) .

A circle of radius 5/sqrt2 is concentric with the ellipse x^(2)/16+y^(2)/9=1 , then the acute angle made by the common tangent with the line sqrt3x-y+6=0 is

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

Length of the focal chord of the ellipse x^2/a^2+y^2/b^2= 1 which is inclined to the major axis at angle theta 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.

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

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

Find the equations of the tangents to the circle x^(2) + y^(2) = 25 inclined at an angle of 60^(@) to the x-axis.

The tangent at any point on the ellipse 16x^(2)+25y^(2) = 400 meets the tangents at the ends of the major axis at T_(1) and T_(2) . The circle on T_(1)T_(2) as diameter passes through

The points of contact of tangents to the circle x^(2)+y^(2)=25 which are inclined at an angle of 30^(@) to the x-axis are