so on this question i have tried completing the square to find the translation but it doesnt seem to work, please tell me if my method is correct or not and how to do it the right way. thanks

YEEEEEET
Oct 13, 2018

#1**+2 **

I'll give this a shot

We can transform the given equation into

9x^2 + 4y^2 = 36

This is an ellipse centered at the origin

We have

9x^2 - 18x + 4y^2 + 16y = c ..... [ complete the square on x , y]

9 ( x^2 - 2x + 1) + 4 ( y^2 + 4y + 4) = c + 9 + 16

9 ( x - 1)^2 + 4 (y + 2)^2 = [ c + 9 + 16 ] divide both sides by 36

(x - 1)^2 / 4 + (y + 2)^2 / 9 = [ c + 9 + 16] / 36

Since we want the right side to be 1, c must = 11

So we have the equation

(x - 1)^2 / 4 + (y + 2)^2 / 9 = 1

So....the translation of the original graph is 1 unit to the right and 2 units down = vector ( 1 , -2 )

So...a = 1 , b = -2 and c = 11

CPhill
Oct 13, 2018