A. Sketches the conic below and find its foci. 36x2 - 9y1 - 288x + 36y + 864 = 0

Question

A.

Sketches the conic below and find its foci. 36x2 - 9y1 - 288x + 36y + 864 = 0 We complete the squares as follows: 9(y2 - 4y) - 36(x2 - 8x) = 864 9(y1 - 4y + ) - 36(x2 - 8x + ) = 864 + 36 - 576 9(y - )2 - 36(x - )2 = (y - )2 - (x - )2/ = 1 This is in the standard form except that x and y are replaced by x - 4 and y - 2. Thus a2 = , b2 = , and c2 = . The hyperbola is shifted four units to the right and two units upward. The foci are (4, ) and (4, -4.71) and the vertices are (4, ) and (4, -4). The asymptotes are y -2 = (2) (x - 4). The hyperbola is sketched in the figure.

Explanation / Answer

4,16,2,4,324,2,4,36,9,2,1,2 fill boxes in order horizontally.

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