`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 :

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

The coordinates of the foci of the ellipse 4x^(2) + 9y^(2) = 1 are

P is a point on the ellipse (x^(2))/(36)+(y^(2))/(9)=1 ; S,S^(1) are the Foci of the ellipse then SP + S^(1)P =

Let the foci of the ellipse (x^(2))/(9) + y^(2) = 1 subtend a right angle at a point P . Then the locus of P is _

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

S_(1) ,S_(2) are two foci of the ellipse x^(2) + 2y^(2) = 2 . P be any point on the ellipse The locus incentre of the triangle PSS_(1) is a conic where length of its latus rectum 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

If P is any point on the ellipse with eccentricity 2/3 and foci F_(1),F_(2) such that PF_(1)+PF_(2)=6 ,then the equation of the ellipse

If the circle whose diameter is the major axis of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a gt b gt 0) meets the minor axis at point P and the orthocentre of DeltaPF_(1)F_(2) lies on the ellipse, where F_(1) and F_(2) are foci of the ellipse, then the square of the eccentricity of the ellipse is