refer to the hyperbola represented by –16y2 – 54x + 9x2 = 63. Write the equations of the asymptotes

Question

tkhunny · Answer

Rearrange:

$(9x^{2} - 54x) - 16y^{2} = 63$

Complete the Square where Possible or Necessary

$9(x^{2} - 6x + 9) - 16y^{2} = 63 + 81$

$9(x - 3)^{2} - 16y^2 = 144$

Divide by 144 and put into Standard Form

$\dfrac{(x - 3)^{2}}{16} - \dfrac{y^{2}}{9} = 1$

$\dfrac{(x - 3)^{2}}{4^{2}} - \dfrac{y^{2}}{3^{2}} = 1$

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