What is the equation of the directrix to the right of the center of (x-1)^2/9 - (y-2)^2/16 = 1?

Express the answer in decimal format.

x =

9514 1404 393

  x = 2.8

Step-by-step explanation:

For a hyperbola of the form ...

  (x -h)^2/a^2 - (y -k)^2/b^2 = 1

the equations of the directrix lines are ...

  x = h ± a^2/√(a^2 +b^2)

Here, we have a^2 = 9, b^2 = 16, h = 1, so the equation of the directrix of interest is ...

  x = 1 +9/√(9+16) = 1 + 9/5

  x = 2.8

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In the attached, the center and foci are shown with a purple X. The (right side) directrix is shown with a green vertical line. The asymptotes are shown as dashed orange lines, and purple construction lines show the relationships between the parts. The purple rectangle is 2a units wide and 2b units high, centered at the center of the hyperbola.

step-by-step explanation:

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