EXAMPLE 7 Sketch the conic below and find its foci. 25x²9y²-150x + 36y + 414 = 0 SOLUTION We complete the squares as follows. 9(x²-4 - 4y - +4 9(y-2 Y 2 25 9(y²4y) 25(x² - 6x) = 414 ✓). 3² ✓ ) ². ✓ ) - 25(x² - 6; - 6x + 19 ²-25(x-3 X- (3,2-√34) and the vertices are (x, y) = 3 9 units upward. The foci are (x, y) = (3,2+√34 - This is in the standard form except that x and y are replaced by x - 3 and y 2. Thus a² = 9 xb² = 25 X, and c² = The hyperbola is shifted three units to the right and two ) and 3,7.8309 ) = 414 + 36 225 (3, -3). The asymptotes are y − 2 = + (x − 3). The hyperbola is t - sketched in the figure. = -225 X = 1 and
EXAMPLE 7 Sketch the conic below and find its foci. 25x²9y²-150x + 36y + 414 = 0 SOLUTION We complete the squares as follows. 9(x²-4 - 4y - +4 9(y-2 Y 2 25 9(y²4y) 25(x² - 6x) = 414 ✓). 3² ✓ ) ². ✓ ) - 25(x² - 6; - 6x + 19 ²-25(x-3 X- (3,2-√34) and the vertices are (x, y) = 3 9 units upward. The foci are (x, y) = (3,2+√34 - This is in the standard form except that x and y are replaced by x - 3 and y 2. Thus a² = 9 xb² = 25 X, and c² = The hyperbola is shifted three units to the right and two ) and 3,7.8309 ) = 414 + 36 225 (3, -3). The asymptotes are y − 2 = + (x − 3). The hyperbola is t - sketched in the figure. = -225 X = 1 and
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:EXAMPLE 7 Sketch the conic below and find its foci.
25x²9y²-150x + 36y + 414 = 0
SOLUTION We complete the squares as follows.
9(x²-4
- 4y - +4
9(y-2
Y
2
25
9(y²4y) 25(x² - 6x) = 414
✓).
3²
✓ ) ².
✓ ) - 25(x² - 6;
- 6x + 19
²-25(x-3
X-
(3,2-√34) and the vertices are (x, y)
=
3
9
units upward. The foci are (x, y) = (3,2+√34
-
This is in the standard form except that x and y are replaced by x - 3
and y 2. Thus a² = 9
xb² = 25
X, and
c² =
The hyperbola is shifted three units to the right and two
) and
3,7.8309 )
= 414 + 36 225
(3, -3). The asymptotes are y − 2 = + (x − 3). The hyperbola is
t
-
sketched in the figure.
= -225 X
= 1
and
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