Question

Find the eccentricity of the hyperbola 144y2 - 12x2
= 144​

Answer 1

Step-by-step explanation:

The equation 16x 2−9y 2 =144.

can be written as 9x 2 − 16y2 =−1

This is of the form a2 x 2− b 2y2−1∴a2 =9,b2 =16⇒a=3,b=4

Length of transverse axis : The length of transverse axis = 2b = 8

Length of conjugate axis : The length of conjugate axis = 2a =6

Eccentricity : (1+ b 2a2) = (1+ 169) = 45

Foci : The co-ordinates of the foci are (0,±be)i.e.,(0,±5)

Vertices : The co-ordinates of the vertices are (0,±b)i.e.,(0,±4)

Length of latus-rectum : The length of latus-rectum = b2a = 42(3)2= 29

Equation of directrices : The equation of directrices are y=±

eb⇒y=± (5/4)4⇒y=± 516