16x^2-32x-9y2+90y-353=0
HELP!!
HELP!!
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16x² - 32x - 9y² + 90y - 353 = 0
regroup terms
(16x² - 32x) - (9y² - 90y) = 353
factor out leading coefficients
16(x² - 2x) - 9(y² - 10y) = 353
complete squares
16(x² - 2x + 1²) - 9(y² - 10y + 5²) = 353 + 16·1² - 9·5²
16(x - 1)² - 9(y - 5)² = 144
divide equation by righthand side
16(x - 1)²/144 - 9(y - 5)²/144 = 144/144
(x - 1)²/9 - (y - 5)²/16 = 1
(x - 1)²/3² - (y - 5)²/4² = 1
By looking at the equation you SHOULD be able to tell that this is a horizontal hyperbola, and
(x−h)²/a² − (y−k)²/b² = 1
center (h, k)
vertices (h±a, k)
c² = a²+b²
foci (h±c, k)
asymptotes y = ±(b/a)x + k∓(b/a)h
center (1, 5)
vertices (1±3, 5) = (-2, 5) and (4, 5)
c² = 3² + 4² = 25
c = 5
foci (1±c, 5) = (-4, 5) and (6, 5)
asymptotes
y = (4/3)x + 5-(4/3)1 = (4/3)x + 11/3
y = -(4/3)x + 5+(4/3)1 = -(4/3)x + 19/3
http://www.flickr.com/photos/dwread/6533…
regroup terms
(16x² - 32x) - (9y² - 90y) = 353
factor out leading coefficients
16(x² - 2x) - 9(y² - 10y) = 353
complete squares
16(x² - 2x + 1²) - 9(y² - 10y + 5²) = 353 + 16·1² - 9·5²
16(x - 1)² - 9(y - 5)² = 144
divide equation by righthand side
16(x - 1)²/144 - 9(y - 5)²/144 = 144/144
(x - 1)²/9 - (y - 5)²/16 = 1
(x - 1)²/3² - (y - 5)²/4² = 1
By looking at the equation you SHOULD be able to tell that this is a horizontal hyperbola, and
(x−h)²/a² − (y−k)²/b² = 1
center (h, k)
vertices (h±a, k)
c² = a²+b²
foci (h±c, k)
asymptotes y = ±(b/a)x + k∓(b/a)h
center (1, 5)
vertices (1±3, 5) = (-2, 5) and (4, 5)
c² = 3² + 4² = 25
c = 5
foci (1±c, 5) = (-4, 5) and (6, 5)
asymptotes
y = (4/3)x + 5-(4/3)1 = (4/3)x + 11/3
y = -(4/3)x + 5+(4/3)1 = -(4/3)x + 19/3
http://www.flickr.com/photos/dwread/6533…