A variable point P on the ellipse of eccentricity e is joined to the foci `S` and `S'`. The eccentricity of the locus of incentre of the triangle `PSS'` is (A) `sqrt((2e)/(1+e))` (B) `sqrt(e/(1+e))` (C) `sqrt((1-e)/(1+e))` (D) `e/(2(1+e))`

int (e ^ (x) dx) / (1 + e ^ (2x)) sqrt (1-e ^ (2x)))

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 Delta PSS is an ellipse whose eccentricity is e_(2), then the value of (1+(1)/(e_(1)))e_(2)

If e_1 and e_2 be the eccentricities of hyperbola and its conjugate, then 1/e^2_1 + 1/e^2_2 = (A) sqrt(2)/8 (B) 1/4 (C) 1 (D) 4

If eccentricities of a parabola and an ellipse are e and e' respectively, then

If eccentricities of a parabola and an ellipse are e and e' respectively, then

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)

A series of concentric ellipses E_1,E_2, E_3..., E_n are drawn such that E touches the extremities of the major axis of E_(n-1), and the foci of E_n coincide with the extremities of minor axis of E_(n-1) If the eccentricity of the ellipses is independent of n, then the value of the eccentricity, is (A) sqrt 5/3 (B) (sqrt 5-1)/2 (C) (sqrt 5 +1)/2 (D) 1/sqrt5

If e_(1) be the eccentricity of a hyperbola and e_(2) be the eccentricity of its conjugate, then show that the point (1/e_(1) , 1/e_(2)) lies on the circle x^(2) + y^(2) = 1 .