Question

PLEASE HELP ME WITH QUESTION 7 SHOW YOUR WORK

Answer 1

Answer:

  (-2, 1) and (6, 1)

Step-by-step explanation:

The standard form equations for a hyperbola are ...

  $\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2} = 1 \\\\\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2} = 1$

The first form opens horizontally; the second opens vertically. Further, the center-focus distance 'c' is given by ...

  $c^2 = a^2 +b^2 \qquad\text{ c = distance from center to focus}$

The attached figure illustrates the relation between the various parameters and the features of the hyperbola.

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7.

Using the above information and the information in the first attachment, we find ...

  (h, k) = (2, 1)

  a = 4, b = 2

The vertices are (h±a, k), so are (2±4, 1) = (-2, 1) and (6, 1).

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The second attachment illustrates the hyperbola and its vertices.