Find the equation of the hyperbola in standard form Foci plu
Find the equation of the hyperbola in standard form: Foci: (plusminus Squareroot 5, 0); asymptotes: y = plusminus 2x
Solution
Focii=(+-sqrt5,0)
and focii=(h+-c,k )
h=0 and k=0
therefore c=sqrt 5
asymptote equation is y= +-(b/a)(x-h) + k
given equation is y=+-2x
on comparing them we get
b/a=2
b=2a
c^2 = a^2 + b^2
5= a^2 + 4a^2
5=5a^2
a=1
b=2a
b=2
therefore required equation is x^2/1 - y^2/4=1
