If `P(x ,y)` is any point on the ellipse `16 x^2+25 y^2=400` and `f_1=(3,0)F_2=(-3,0)` , then find the value of `P F_1+P F_2dot`

P(x,y) is any point on ellipse 16x^(2)+25y^(2) =400 . If F_(1)-=(3,0) and F_(2) -=(-3,0) , then prove that PF_(1)+PF_(2) is constant and find its value .

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

P is any variable point on the ellipse 4x^(2) + 9y^(2) = 36 and F_(1), F_(2) are its foci. Maxium area of trianglePF_(1)F_(2) ( e is eccentricity of ellipse )

Co-ordinates of a point P((pi)/(3)) on the ellipse 16x^(2) + 25y^(2) = 400 are

Let P be a variable point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with foci F_1" and "F_2 . If A is the area of the trianglePF_1F_2 , then the maximum value of A is

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 f(y) = 2y^(2) + by + c and f(0) = 3 and f(2) = 1, then the value of f(1) is

P is any point on the hyperbola x^(2)-y^(2)=a^(2) . If F_1 and F_2 are the foci of the hyperbola and PF_1*PF_2=lambda(OP)^(2) . Where O is the origin, then lambda is equal to