Home
Class 12
MATHS
If the normal at an end oof a lasrurectu...

If the normal at an end oof a lasrurectum of an ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1` pases through one extremly of the minor axis, show that the eccentricity of the ellipse is given by `e^(4)+e^(2)-1=0` or `e^(2)=sqrt((5)-1/(2))`

Promotional Banner

Similar Questions

Explore conceptually related problems

If the normal at one end of the latus rectum of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 passes through one end of the minor axis, then prove that eccentricity is constant.

If the normal at one end of the latus rectum of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 passes through one end of the monor axis, then prove that eccentricity is constant.

If the normals at an end of a latus rectum of an ellipse passes through the other end of the minor axis, then prove that e^(4) + e^(2) =1.

The eccentricity of the ellipse x^(2)+4y^(2)+8y-2x+1=0 , is

The normal at an end of a latus rectum of the ellipse x^2/a^2 + y^2/b^2 = 1 passes through an end of the minor axis if (A) e^4+e^2=1 (B) e^3+e^2=1 (C) e^2+e=1 (D) e^3+e=1

Chords of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are drawn through the positive end of the minor axis. Then prove that their midpoints lie on the ellipse.

the eccentricity of an ellipse (x^(2))/(a^(2))+(y^(2))=1 whose latus rectum is half of its minor axes , is

S and T are the foci of the ellipse x^2/a^2+y^2/b^2 = 1 and B is an end of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is e then find value of 4e

The foci of an ellipse are (-2,4) and (2,1). The point (1,(23)/(6)) is an extremity of the minor axis. What is the value of the eccentricity?

Eccentricity of the ellipse 4x^2+y^2-8x+2y+1=0 is