Question

in each of the hyperbola ,find the coordinates of the vertices and the foci,the eccentricity the length of the axes and the latus rectum:- x^2-4y^2= 4​

Answer 1

Step-by-step explanation:

x²-4y²=4

divide all terms with 4

(x²/4)-(4y²/4)=4/4

(x²/4)-y²=1

(x²/2²)-y²/1²=1

a=2,b=1

vertices=(a,0) and (-a,0)

=(2,0)and(-2,0)

ecentricity (e)=√1+b²/a²

=√[1+(1/4)]

=√(4+1/4)

√(5/4)

=√5/2

foci =(ae,0)and(-ae,0)

=(2×√5/2,0)and(-2×√5/2,0)

=(√5,0) and (-√5,0)

length of transverse axis=2a units

=2×2

=4 units

length of conjugate axis =2b units

=2×1

=2units

length of latus rectum=2b²/a

=2×(1²/2)

=1sq.units