5. (a) Find the parabola's vertex, focus, di i. (y + 2)2 = 8(x - 1)

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter7: Conic Sections
Section7.3: Hyperbolas
Problem 2E
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5. (a) Find the parabola's vertex, focus, directrix and hence sketch the parabola, given that
i. (y + 2)2 = 8(x - 1)
ii. (x + 1)² = -4(y - 3)
2
(b) Find the foci, vertices, center and hence sketch each of the following ellipses.
i. (x-4)² + (x-3)² = 1
16
(c) Find the foci, vertices, center, asymptotes and hence sketch each of the following
hyperbolas.
i, (y+2)²
i. 2x² + 2y² + 6x
8y + 12 = 0
ii. y² - 4y - 8x - 12 = 0
ii. (x+3)² + (x+2)² = 1
9
1
S
ii. (x-2)²
16
fe
(d) Find the center, foci, vertices, asymptotes, radius, as appropriate, and sketch the conic
section given that:
-1
iii. 4x² 48x +9y² + 72y + 144 = 0
iv. x² - y² + 4x - 6y = 6
2
Transcribed Image Text:5. (a) Find the parabola's vertex, focus, directrix and hence sketch the parabola, given that i. (y + 2)2 = 8(x - 1) ii. (x + 1)² = -4(y - 3) 2 (b) Find the foci, vertices, center and hence sketch each of the following ellipses. i. (x-4)² + (x-3)² = 1 16 (c) Find the foci, vertices, center, asymptotes and hence sketch each of the following hyperbolas. i, (y+2)² i. 2x² + 2y² + 6x 8y + 12 = 0 ii. y² - 4y - 8x - 12 = 0 ii. (x+3)² + (x+2)² = 1 9 1 S ii. (x-2)² 16 fe (d) Find the center, foci, vertices, asymptotes, radius, as appropriate, and sketch the conic section given that: -1 iii. 4x² 48x +9y² + 72y + 144 = 0 iv. x² - y² + 4x - 6y = 6 2
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