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 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 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.

Find the value of k if 4x+y+k=0 is a tangent to the ellipse x^2+3y^2=3 .

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

let P be a point the first quadrant lying on the ellipse 9x^(2) +16y^(2) =144, such that the tangent at P to the ellipse is inclined at an angle 135^(@) to the positive direction of x-axis Then the coordinates of P are

The tangent to the ellipse 3x^(2) +16y^(2) =12 ,at the point (1,3//4) , interects the curve y^(2) +x= 0 at

The length of the major axis of the ellipse (x-3)^(2)/4+(y-2)^(2)/9=1 is