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

 Find the equation of the hyperbola in standard form: Foci: (plusminus Squareroot 5, 0); asymptotes: y = plusminus 2xSolutionFocii=(+-sqrt5,0) and focii=(h+-c,k

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