If `e=(3)^(1/2)/2` , its length of latusrectum is

If the parabola y^(2)=4ax passes through (3, 2). Then the length of its latusrectum, is

Let the equation of ellipse be x^(2)/(a^(2)+1)=y^(2)/(a^(2)+2)=1 Statement 1 If eccentricity of the ellipse be 1/sqrt6 , then length of latusrectum is 10/sqrt6 . Statement 2 Length of latusrectum= (2(a^(2)+1))/(sqrt(a^(2)+2))

The parabola y^(2)=4ax passes through the point (2, -6), then the length of its latusrectum, is

If the focus and directrix of a parabola are (3,-4) and x+y+7=0 then its length of latusrectum is

if the line x- 2y = 12 is tangent to the ellipse (x^(2))/(b^(2))+(y^(2))/(b^(2))=1 at the point (3,(-9)/(2)) then the length of the latusrectum of the ellipse is

If x+y=0,x-y=0 are tangents to a parabola whose focus is (1,2) Then the length of the latusrectum of the parabola is equal

The eccentricity of the ellipse if the distance between the foci is equal to the length of the latusrectum ,is