0 A Review Of Basic Algebra 1 Equations And Inequalities 2 Functions And Graphs 3 Functions 4 Polynomial And Rational Functions 5 Exponential And Logarithmic Functions 6 Linear Systems 7 Conic Sections And Quadratic Systems 8 Sequences, Series, And Probability Chapter7: Conic Sections And Quadratic Systems
7.1 The Circle And The Parabola 7.2 The Ellipse 7.3 The Hyperbola 7.4 Solving Nonlinear Systems Of Equations 7.CR Chapter Review 7.CT Chapter Test 7.CM Cumulative Review Exercises Section7.1: The Circle And The Parabola
Problem 1SC Problem 2SC Problem 3SC Problem 4SC Problem 5SC Problem 6SC Problem 7SC: Find the vertex and yintercepts of the parabola with an equation of y2x+2y=3. Then graph it. Problem 8SC Problem 9SC Problem 1E Problem 2E Problem 3E Problem 4E Problem 5E Problem 6E: Determine whether the graph of the parabola opens upward, downward, to the left, or to the right.... Problem 7E Problem 8E: Determine whether the graph of the parabola opens upward, downward, to the left, or to the right.... Problem 9E: Fill in the blanks. A parabola is the set of all points in a plane equidistant from a line, called... Problem 10E Problem 11E Problem 12E Problem 13E Problem 14E Problem 15E Problem 16E Problem 17E Problem 18E Problem 19E Problem 20E Problem 21E Problem 22E Problem 23E Problem 24E Problem 25E Problem 26E Problem 27E Problem 28E Problem 29E Problem 30E Problem 31E: Find an equation in standard form of each parabola described. Vertex at (0,0); focus at (0,3) Problem 32E: Find an equation in standard form of each parabola described. Vertex at (0,0); focus at (0,3) Problem 33E: Find an equation in standard form of each parabola described. Vertex at (0,0); focus at (3,0) Problem 34E: Find an equation in standard form of each parabola described. Vertex at (0,0); focus at (3,0) Problem 35E: Find an equation in standard form of each parabola described. Vertex at (3,5); focus at (3,2) Problem 36E: Find an equation in standard form of each parabola described. Vertex at (3,5); focus at (3,5) Problem 37E: Find an equation in standard form of each parabola described. Vertex at (3,5); focus at (3,2) Problem 38E: Find an equation in standard form of each parabola described. Vertex at (3,5); focus at (6,5) Problem 39E: Find an equation in standard form of each parabola described. Vertex at (0,2); directrix at y=3 Problem 40E: Find an equation in standard form of each parabola described. Vertex at (3,4); focus at y=2 Problem 41E: Find an equation in standard form of each parabola described. Vertex at (1,5); directrix at x=1 Problem 42E: Find an equation in standard form of each parabola described. Vertex at (3,5); directrix at x=6 Problem 43E: Find an equation in standard form of each parabola described. Vertex at (2,2); passes through (0,0) Problem 44E: Find an equation in standard form of each parabola described. Vertex at (2,2); passes through (0,0) Problem 45E: Find an equation in standard form of each parabola described. Vertex at (4,6); passes through (0,3) Problem 46E: Find an equation in standard form of each parabola described. Vertex at (2,3); passes through (0,3) Problem 47E: Find an equation in standard form of each parabola described. Vertex at (6,8); passes through (5,10)... Problem 48E: Find an equation in standard form of each parabola described. Vertex at (2,3); passes through... Problem 49E: Find an equation in standard form of each parabola described. Vertex at (3,1); passes through (4,3)... Problem 50E: Find an equation in standard form of each parabola described. Vertex at (4,2); passes through (3,0)... Problem 51E: Write each parabola in standard form and graph it. y=x2+4x+5 Problem 52E: Write each parabola in standard form and graph it. 2x212x7y=10 Problem 53E: Write each parabola in standard form and graph it. y2+4x6y=1 Problem 54E: Write each parabola in standard form and graph it. x22y2x=7 Problem 55E: Write each parabola in standard form and graph it. y24y=4x8 Problem 56E: Write each parabola in standard form and graph it. y2+2x2y=5 Problem 57E: Write each parabola in standard form and graph it. y24y=8x+20 Problem 58E: Write each parabola in standard form and graph it. y22y=9x+17 Problem 59E: Write each parabola in standard form and graph it. x26y+22=4x Problem 60E: Write each parabola in standard form and graph it. 4y24y+16x=7 Problem 61E: Write each parabola in standard form and graph it. 4x24x+32y=47 Problem 62E Problem 63E Problem 64E Problem 65E Problem 66E Problem 67E Problem 68E: Ripples in a pond When a stone is thrown into the center of a pond, the ripples spread out in a... Problem 69E Problem 70E Problem 71E: Meshing gear For design purpose, the large gear is described by the circle x2+y2=16. The smaller... Problem 72E Problem 73E Problem 74E: Searchlight reflectors A parabolic mirror reflect light in a beam when the light source is placed at... Problem 75E: Writing equation of the parabolas Derive the equation of the parabolic arch shown. Problem 76E: Projectiles The cannonball in the illustration follows the parabolic trajectory y=30xx2. How far... Problem 77E: Satellite antennas The cross section of the satellite antenna in the illustration is a parabola... Problem 78E: Design of a satellite antenna The cross section of the satellite antenna shown is a parabola with... Problem 79E Problem 80E: Operating a resort A resort owner plans to build and rent n cabins for d dollars per week. The price... Problem 81E: Design of a parabolic reflector Find the outer diameter The length AB of the parabolic reflector... Problem 82E: Design of a suspension bridge The cable between the tower of the suspension bridge shown in the... Problem 83E: Gateway Arch The gateway Arch in St.Louis has a shape that approximates a parabola. See the... Problem 84E: Building tunnels A construction firm plans to build a tunnel whose arch is in the shape of parabola.... Problem 85E Problem 86E Problem 87E Problem 88E Problem 89E Problem 90E Problem 91E Problem 92E Problem 93E Problem 94E Problem 95E Problem 96E Problem 97E Problem 98E: In Exercises 95-98, match the equation of the parabola with its graph. y2=9x a. b. c. d. Problem 99E Problem 100E Problem 101E Problem 102E Problem 14E
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Sketch the conic sections. Indicate the foci, and show your work:
A) 4x 2 +3y 2 +8x -6y =5
B) x 2 -3y 2 +8x -6y +4=0
Curve that is obtained by the intersection of the surface of a cone with a plane. The three types of conic sections are parabolas, ellipses, and hyperbolas. The main features of conic sections are focus, eccentricity, and directrix. The other parameters are principal axis, linear eccentricity, latus rectum, focal parameter, and major and minor axis.
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