Let `F_1,F_2` be two foci of the ellipse `x^2/(p^2+2)+y^2/(p^2+4)=1` . Let P be any point on the ellipse , the maximum possible value of `PF_1 . PF_2 -p^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 :

If F_(1) and F_(2) are the feet of the perpendiculars from foci S_(1) and S_(2) of the ellipse (x^(2 /(25 +y^(2 /(16 =1 on the tangent at any point P of the ellipse,then the minimum value of S_(1 F_(1 +S_(2 F_(2 is 1) 2, 2) 3, 3) 6, 4) 8

Let F_(1),F_(2) are the foci of the ellipse 4x^(2)+9y^(2)=36 and P is a point on ellipse such that PF_(1)=2PF_(2), then the area of triangle PF_(1)F_(2) is

Let F1,F_(2) be two focii of the ellipse and PT and PN be the tangent and the normal respectively to the ellipse at ponit P.then

If the normal to the ellipse x^2/25+y^2/1=1 is at a distance p from the origin then the maximum value of p is

Let d_1a n dd_2 be the length of the perpendiculars drawn from the foci Sa n dS ' of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 to the tangent at any point P on the ellipse. Then, S P : S^(prime)P= d_1: d_2 (b) d_2: d_1 d1 2:d2 2 (d) sqrt(d_1):sqrt(d_2)

P is any point on the ellipise (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and S and S are its foci, then maximum value of the angle SPS is

Let F_1 (0, 3) and F_2 (0, -3) be two points and P be any point on the ellipse 25x^2 + 16y^2= 400 , then value of (PF_1+ PF_2) is