SOLUTION: Find an equation for the hyperbola with vertices (2,0) and (-2,0) and asymptote y=1/2x (A) 4x^2-y^2=4 (B) x^2-4y^2=4 (C) x^2-y^2=4 (D) x^2+4y^2=4 Thank you very much

Question 31819: Find an equation for the hyperbola with vertices (2,0) and (-2,0) and asymptote y=1/2x
(A) 4x^2-y^2=4
(B) x^2-4y^2=4
(C) x^2-y^2=4
(D) x^2+4y^2=4
Thank you very much!
Answer by mukhopadhyay(490) (Show Source): You can put this solution on YOUR website!
b/a=1/2 (from asymptote)
Vertices are at (2,0) and (-2,0); a=2;
b/a=2 => b=1
=> center is at (0,0) and transverse axis is x-axis
So, standard equation is:
x^2/a^2 - y^2/b^2 = 1
Required equation is
x^2/4 - y^2/1 = 1
=>x^2-4y^2=4
Correct option is B

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