Consider an ellipse `E ,(x^2)/(a^2)+(y^2)/(b^2)=1` , centered at point `O` andhaving `A Ba n dC D` 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 `O C S_1` is unit, and `O S_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

Consider an ellipse E: x^(2)/a^(2)+y^(2)/b^(2)=1 , centered at point 'O' and having AB and CD as its major and minor axes respectively if S_1 be one of the focus of the ellipse, radius of the incircle of DeltaOCS_1 be 1 unit and OS_1=6 units. Q. if the ellipse (E) is ∆sq unit, then the value of 4 Delta is

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

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.

A tangent having slope of -4/3 to the ellipse (x^2)/(18)+(y^2)/(32)=1 intersects the major and minor axes at point Aa n dB , respectively. If C is the center of the ellipse, then the area of triangle A B C is 12s qdotu n i t s (b) 24s qdotu n i t s 36s qdotu n i t s (d) 48s qdotu n i t s

Consider an ellipse x^2/25+y^2/9=1 with centre c and a point P on it with eccentric angle pi/4. Nomal drawn at P intersects the major and minor axes in A and B respectively. N_1 and N_2 are the feet of the perpendiculars from the foci S_1 and S_2 respectively on the tangent at P and N is the foot of the perpendicular from the centre of the ellipse on the normal at P. Tangent at P intersects the axis of x at T.

Point 'O' is the centre of the ellipse with major axis AB & minor axis CD. Point F is one focus of the ellipse. If OF = 6 & the diameter of the inscribed circle of triangle OCF is 2, then find the product (AB).(CD)

Consider an ellipse (x^(2))/(25)+(y^(2))/(16)=1. A circle passes through a focus and has its centre on y=0 and touches the ellipse at A and S is focus,then