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After graphing the C1 and playing around on desmos i figured out a= 3

but can someone explain to me why please because i dont see the correlation between the new asymptotes and (x-3)^2

thank you

YEEEEEET Dec 30, 2018

#1**+2 **

This is a hyperbola centered at the origin intersecting the x axis

The equations of the asymptotes are

y = (2/3)x and y = (-2/3)x

Notice that these lines intersect at the hyperbola's center.....if we set these equal, we can verify that the origin is the center

(2/3)x = (-2/3)x

x = -x

2x = 0

x = 0

And putting this value of x into either linear equation gives y =0

So...the center of C1 is (0,0)

Therefore....set

(2/3)x - 2 = (-2/3)x + 2

(4/3)x = 4 Implies that x = 3

And putting this value back into either equation gives y = (2/3)(3) - 2 = 0

So....the center of C2 is (3, 0).....so C2 is the translation of C1 - 3 units to the right

So....as you found YEEEEEET.....a = 3.....!!!!

CPhill Dec 31, 2018