SOLUTION: Give the coordinates of the center, foci and vertices with equation 9x2 - 4y2 - 90x

SOLUTION: Give the coordinates of the center, foci and vertices with equation 9x2 - 4y2 - 90x - 32y = -305.

Question 1119419: Give the coordinates of the center, foci and vertices with equation 9x2 - 4y2 - 90x - 32y = -305.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

(1) Factor out the leading coefficients in both x and y.

(2) Complete the square in both x and y, keeping the equation balanced.

(3) Divide both sides by the constant on the right.

This is a hyperbola with the branches opening up and down; the standard form of the equation is

(h,k) is the center; a is the distance from the center to each end of the transverse axis (between the two vertices); b is the distance from the center to each end of the conjugate axis.

So in this hyperbola the center is (5,-4), and the distance from the center to each vertex is 6; that makes the two vertices (5,-10) and (5,2).

c is the distance from the center to each focus; for a hyperbola, . So for this hyperbola, . The two foci are then (5,-4-2*sqrt(13)) and (5,-4+2*sqrt(13)).

Answers:
center (5,-4)
vertices: (5,-10) and (5,2)
foci: (5,-4-2*sqrt(13)) and (5,-4+2*sqrt(13))

A graph....

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