Question

A hyperbola has axes along coordinate axes. Its transverse axis is 2a and it passes through (h,k) then its eccentricity is-
Please give detailed explanation .Thanks for ur help

Answer 1

Answer:

Step-by-step explanation:

Standard Equation

x2/a2 – y2/b2 = 1

-x2/a2 + y2/b2 = 1

Centre

(0,0)

(0, 0)

Equation of Transverse axis

y = 0

x= 0

Equation of Conjugate axis

x = 0

y = 0

Length of Transverse axis

2a

2b

Length of Conjugate axis

2b

2a

Vertices

(±a, 0)

(0, ±b)

Foci

(±ae, 0)

(0, ±be)

Equation of directrix

x = ±a/e

y = ±b/e

Eccentricity

e = √(a2+b2)/a2

e = √(a2+b2)/b2

Parametric Coordinates

(a sec θ, b tan θ)

(a tan θ, b sec θ)

Length of Latus Rectum

2b2/a

2a2/b

Tangent at the vertices

x = ±a

y = ±b