F is one of the foci of the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` with O as centre. `bar(AB)` and `bar(CD)` are major and minor axes respectively. If OF=6 and the diameter of the incircle of triangle OCF is 2. The values of a & b are

Consider an ellipse E,(x^(2))/(a^(2))+(y^(2))/(b^(2))=1, centered at point O andhaving AB and CD as its major and minor axes,respectively.If S_(1) is one of the focus of the ellipse,the radius of the incircle of triangle OCS_(1) is unit,and OS_(1)=6 units, then the value of (a-b)/(2) is

An ellipse E,(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , centred at point O has AB and CD as its major and minor axes, respectively. Let S_(1) be one of the foci of the ellipse, the radius of the incircle of triangle OCS_(1) be 1 unit, and OS_(1)=6 units The perimeter of DeltaOCS_(1) is

A tangent having slope of -(4)/(3) to the ellipse (x^(2))/(18)+(y^(2))/(32)=1 intersects the major and minor axes at points A and B, respectively.If C is the center of the ellipse,then find area of triangle ABC.

For the ellipse,(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 the equation of the diameter conjugate ax-by=0 is-

If the length of the major axis of the ellipse ((x^(2))/(a^(2)))+((y^(2))/(b^(2)))=1 is three times the length of minor axis, its accentricity is

S and T are the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and B is an end of the minor axis.If STB is an equilateral triangle,the eccentricity of the ellipse is e then find value of 4e