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# Parabola translation

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3  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

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.....!!!!   Dec 31, 2018
edited by CPhill  Dec 31, 2018
#2
+1

ohhh i was finding it weird as the equation for asymptotes are +-b/a but as i followed up to the part where u explained how asymptotes can find origin i immediately clicked on. thanks a lot!!!

YEEEEEET  Dec 31, 2018
#3
+1

OK....this one was kinda' interesting....!!!   CPhill  Dec 31, 2018