Introduction To Hyperbola | Eccentricity| Latus Rectum|Examples

If x^2-y^2sec^2theta=10 be a hyperbola and x^2sec^2theta+y^2=5 be an ellipse such that the eccentricity of hyperbola= sqrt(5) eccentricity of ellipse then find the length of latus rectum of ellipse

In the hyperbola 4x^2 - 9y^2 = 36 , find the axes, the coordinates of the foci, the eccentricity, and the latus rectum.

Find the equation of the hyperbola , the length of whose latus rectum is 4 and the eccentricity is 3.

If the extremities of the latus rectum of the hyperbola with positive coordinates lie on the parabola x^(2) = 3(y + 3) , then length of the latus rectum of the hyperbola when its eccentricity is sqrt(3) is

The difference between the length 2a of the trans­verse axis of a hyperbola of eccentricity e and the length of its latus rectum is

Find the equation of hyperbola whose conjugate axis = latus-rectum = 8 ,

Find the equation of the hyperbola, the length of whose latus rectum is 8 , eccentricity is 3/sqrt(5) and whose transverse and conjugate axes are along the x and y axes respectively.

If the latus rectum of a hyperbola forms an equilateral triangle with the vertex at the center of the hyperbola,then find the eccentricity of the hyperbola.

Equation of hyperbola is standard from having latus rectum = 9 and eccentricity = 5/4 is