A circle, of radius r, is concentric with the ellipse , 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)))` and find its length

A circle of radius r is concentric with the ellipse (x^2)/(a^(2))+(y^2)/(b^(2))=1 .Then inclination of common tangent with major axis is

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

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

Two circles of radius r_(1) and r_(2) touches externally at point A have a common tangent PQ. Then find the value of PQ^(2) .

If the tangent to the curve xy+ax+by=0 at (1,1) is inclined at an angle tan ^(-1)2 with x . axis,then find a and b?

Find the sum sum_(r =1)^(oo) tan^(-1) ((2(2r -1))/(4 + r^(2) (r^(2) -2r + 1)))

Two circles C(0,r) and C(O',r') touch extemally.Show that the length of a common tangent (not through the point of contact of the circles ) is 2sqrt(rr)'

The length of the common chord of the circles (x-a)^(2)+y^(2)=r^(2) and x^(2)+(y-b)^(2)=r^(2) is

An ellipse is cutout of a circle of radius a,the major axis of the ellipse coincides with one of the diameter of the circle while the minor axis is equal to 2b .Prove that the area of the remaining part equals that of the ellipse with the semi axes a and a -b .