College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Rational Functions And Conics
Section4.3: Conics
Problem 53E
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KFUPM – PREP MATH PROGRAM – MATH002 – TERM 203
12.2 & 12.3 Recitation Exercises
1. Find the center, the vertices, foci, and eccentricity of the ellipse given by the
equation
a) 3x2 + 2y2 – 6x + 12y
= -15
b) 3y2 + 2x2 – 6y + 12x = -15
2.
a) Find the equation of the ellipse that has vertices at (3,8) and (3, -2), and
foci at (3,6) and (3,0).
b) Find the equation in standard form, of the ellipse with foci at (-1,2) and
(3,2) that passes through the point (3,5).
(x+1)2
(y-2)2
3. Find the points of intersection of the ellipse
= 1, and the
16
hyperbola
(x+1)²
(y-2)2
= 1:
16
a)
By solving the system of nonlinear equations.
b) By graphing.
4. Find the equation in standard form of the hyperbola with vertices (-1,0) and
V5
(-1,–4), and eccentricity e =
2'
5. Write the following equations in standard form and identify the corresponding
conics
a)
x² – 4x + y2 + 2y + 2 = 0.
b)
2x2 – 8x – 2y? – 4y = 0.
c)
27x2 + 36y2 + 18x + 36y – 96 = 0.
Transcribed Image Text:KFUPM – PREP MATH PROGRAM – MATH002 – TERM 203 12.2 & 12.3 Recitation Exercises 1. Find the center, the vertices, foci, and eccentricity of the ellipse given by the equation a) 3x2 + 2y2 – 6x + 12y = -15 b) 3y2 + 2x2 – 6y + 12x = -15 2. a) Find the equation of the ellipse that has vertices at (3,8) and (3, -2), and foci at (3,6) and (3,0). b) Find the equation in standard form, of the ellipse with foci at (-1,2) and (3,2) that passes through the point (3,5). (x+1)2 (y-2)2 3. Find the points of intersection of the ellipse = 1, and the 16 hyperbola (x+1)² (y-2)2 = 1: 16 a) By solving the system of nonlinear equations. b) By graphing. 4. Find the equation in standard form of the hyperbola with vertices (-1,0) and V5 (-1,–4), and eccentricity e = 2' 5. Write the following equations in standard form and identify the corresponding conics a) x² – 4x + y2 + 2y + 2 = 0. b) 2x2 – 8x – 2y? – 4y = 0. c) 27x2 + 36y2 + 18x + 36y – 96 = 0.
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