If e, e' be the eccentricity of two conics S=0 and S'=0 and if `e^2+e'^2=3`, then both S and S' can be

If e and e' be the eccentricities of two conics S=0 and S'=0 and if e^(2)+e'^(2)=3 , then both S and S' can be

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))

Let E1 and E2, be two ellipses whose centers are at the origin.The major axes of E1 and E2, lie along the x-axis and the y-axis, respectively. Let S be the circle x^2 + (y-1)^2= 2 . The straight line x+ y =3 touches the curves S, E1 and E2 at P,Q and R, respectively. Suppose that PQ=PR=[2sqrt2]/3 .If e1 and e2 are the eccentricities of E1 and E2, respectively, then the correct expression(s) is(are):

If e is the eccentricity, l is the semi latus-rectum and S. S^(1) are foci of the hyperbola 9x^(2)-16y^(2)+72x-32y=16 then ascending order of l, e SS^(1) is

If both the distinct roots of the equation |sinx|^2+|sinx|+b=0in[0,pi] are real, then the values of b are [-2,0] (b) (-2,0) [-2,0] (d) non eoft h e s e

If both the distinct roots of the equation |sinx|^2+|sinx|+b=0in[0,pi] are real, then the values of b are [-2,0] (b) (-2,0) [-2,0] (d) non eoft h e s e

Let E_(1) and E_(2) be two ellipse whsoe centers are at the origin. The major axes of E_(1) and E_(2) lie along the x-axis , and the y-axis, respectively. Let S be the circle x^(2)+(y-1)^(2)=2 . The straigth line x+y=3 touches the curves, S, E_(1) and E_(2) at P,Q and R, respectively . Suppose that PQ=PR=(2sqrt(2))/(3) . If e_(1) and e_(2) are the eccentricities of E_(1) and E_(2) respectively, thent hecorrect expression (s) is (are)

If 2s-e=32 and 2e-d=10 , what is the average of d and e?

Consider the conic ex^(2)+piy^(2)-2e^(2)x-2pi^(2)y+e^(3)+pi^(3)= pie . Suppose P is any point on the conic and S_(1),S_(2) are the foci of conic, then the maximum value of (PS_(1)+PS_(2)) is -

The directrix of a conic section is the line 3x+4y=1 and the focus S is (-2, 3). If the eccentricity e is 1/sqrt(2) , find the equation to the conic section.