Question

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

Answer 1

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

\(\dfrac{(x - 3)^{2}}{16} - \dfrac{y^{2}}{9} = 1\)

\(\dfrac{(x - 3)^{2}}{4^{2}} - \dfrac{y^{2}}{3^{2}} = 1\)

Okay, there's your one free one. Show us what to do from here.