If P is a variable point on the ellipse `x^2/a^2 + y^2/b^2 = 1` whose focii are S' and S and `e_1` is the eccentricity and the locus of the inceose centre of `DeltaPSS` is an ellipse whose eccentricity is `e_2`, then the value of `(1+ 1/e_1) e_2`

If P(alpha,beta) is a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with foci Sa n dS ' and eccentricity e , then prove that the area of S P S ' is basqrt(a^2-alpha^2)

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 )

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 )

Let S and S' be the fociof the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentricity is e. P is a variable point on the ellipse. Consider the locus the incenter of DeltaPSS' The eccentricity of the locus of the P is

Let S and S'' be the fociof the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentricity is e. P is a variable point on the ellipse. Consider the locus the incenter of DeltaPSS'' The eccentricity of the locus of the P is

The normal at a variable point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 of eccentricity e meets the axes of the ellipse at Q and R .Then the locus of the midpoint of QR is a conic with eccentricity e' such that e' is independent of e(b)e'=1e'=e(d)e'=(1)/(e)