Answer in standard form please Thank you Find equation of of

Answer in standard form, please. Thank you.

Find equation of of a hyperbola the the given conditions satisfying Asymptotes y x, y -x: one vertex (2, 0) The equation of the hyperbola is r in standard form.

Solution

y = x/2 ; y = -x/2 ; vertex ( 2, 0)

asymtotes passes throough origin : centre is (0,0)

x^2 /a^2 - y^2/b^2 = 1

vertex ( 2, 0) : 4/a^2 - 0 =1

a = 2

and from asymtotes : b/a = 1/2

b = a/2 = 2/2 = 1

So, x^2/4 - y^2 /1 =1