Let `P` be a point on the ellipse `x^2/100 + y^2/25 =1` and the length of perpendicular from centre of the ellipse to the tangent to ellipse at `P` be `5sqrt(2) and F_1 and F_2` be the foci of the ellipse, then `PF_1.PF_2`.

The Foci of the ellipse (x^(2))/(16)+(y^(2))/(25)=1 are

Eccentric angle of a point on the ellipse x^(2)/4+y^(2)/3=1 at a distance 2 units from the centre of ellipse is:

If P is a point on the ellipse (x^(2))/(36)+(y^(2))/(9)=1 , S and S ’ are the foci of the ellipse then find SP + S^1P

Let d be the perpendicular distance from the centre of the ellipse x^2/a^2+y^2/b^2=1 to the tangent drawn at a point P on the ellipse. If F_1 & F_2 are the two foci of the ellipse, then show the (PF_1-PF_2)^2=4a^2[1-b^2/d^2] .

If F_1 and F_2 are the feet of the perpendiculars from the foci S_1a n dS_2 of the ellipse (x^2)/(25)+(y^2)/(16)=1 on the tangent at any point P on the ellipse, then prove that S_1F_1+S_2F_2geq8.

If F_1" and "F_2 be the feet of perpendicular from the foci S_1" and "S_2 of an ellipse (x^2)/(5)+(y^2)/(3)=1 on the tangent at any point P on the ellipse then (S_1F_1)*(S_2F_2) is

The locus of the foot of the perpendicular from the foci an any tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

If P is a point on the ellipse (x^(2))/16+(y^(2))/25=1 whose foci are S and S', then PS+PS'=8.

F_(1) and F_(2) are the two foci of the ellipse (x^(2))/(9) + (y^(2))/(4) = 1. Let P be a point on the ellipse such that |PF_(1) | = 2|PF_(2)| , where F_(1) and F_(2) are the two foci of the ellipse . The area of triangle PF_(1)F_(2) is :

F_(1) and F_(2) are the two foci of the ellipse (x^(2))/(9) + (y^(2))/(4) = 1. Let P be a point on the ellipse such that |PF_(1) | = 2|PF_(2)| , where F_(1) and F_(2) are the two foci of the ellipse . The area of triangle PF_(1)F_(2) is :