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Ellipse

Precalc conic review station activity

Subject: 
Trigonometry
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Conic sections
Analytic geometry
Curves
Orbits
Hyperbola
Semi-minor axis
Ellipse
focus
Parabola
eccentricity
Semi-major axis
Asymptote

Station 1: Write the equation for a circle with a diameter that has endpoints of (1, 5) and (12, -2). Station 2: Find an equation for the hyperbola with center at (1, -2) and vertices at (4, -2) and (-2, -2), with a conjugate axis of length 10. Station 3: Determine an equation for the parabola with focus (3, 6) and directrix y = -2. Station 4: Find the vertex, focus, directrix and focal width of the parabola with equation , then graph it. Station 5: Determine an equation for the parabola with vertex (2, 4) and focus (0, 4). Station 6: Determine the major and minor vertices, center, and foci of the ellipse , then graph it. Station 7: Determine what type of conic is, then identify all key information and graph it. Station 8:

alg2 review

Subject: 
Algebra
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Elementary algebra
Conic sections
Curves
equations
polynomials
Cubic function
Parabola
Logarithm
Ellipse
Tangent
quadratic equation
Linear differential equation

H/GT Algebra II - Semester Exam Final Review 1.) Solve 4 264 16 1 0b b? ? ? 2.) What is the vertex of 23 24 5y x x? ? ?? 3.) Graph 22( 1) 1y x? ? ? 4.) Solve 25 19 4n n? ? 5.) Write an equation of a parabola that passes through the points (0, 2), (-2, 6), and (6, 14). 6.) Write the equation for the graph below. 7.) Write an equation of a parabola (general form) with vertex (0, 0) and directrix y = 2. 8.) Find the vertex of 24 4x y y? ? 9.) Graph 2 3y x? ? 10.) Write an equation of a circle with center (4, -3) and radius 5. (General form) 11.) Find the center and radius: 2 2 8 4 12 0x y x y? ? ? ? ?

Analytical Geometry Study Guide

Subject: 
Trigonometry
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geometry
Algebraic geometry
Conic sections
Curves
Analytic geometry
Hyperbola
Ellipse
Asymptote
Parabola
Polar coordinate system
Semi-major axis
Linear equation

Analytical Geometry Formulas and Equations: Midpoint Formula of P(x1, y1), P?(x2, y2): Distance Formula of P(x1, y1), P?(x2, y2): Slope-Intercept Form y = mx + b Point-Slope Form y2 - y1 = m(x2 - x1) General Form of a Line Ax + By + C = 0 Standard Form of a Line Ax + By = C *Slope of line is (?A/B) Slope of P(x1, y1), P?(x2, y2): *Slopes of parallel lines are equal *Slopes of perpendicular lines are opposite and reciprocal Directed Distance from line Ax+By+C=0 to point P(x1, y1) * The sign of the denominator is the same sign as ?B? in the line. *The directed distance will be positive if the point P is above the line, and negative if P is below the line. Directed Distance Between 2 Parallel Lines *The parallel lines are: Ax+By+C & Ax+By+C?

Analytical Geometry Study Guide

Subject: 
Trigonometry
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geometry
Algebraic geometry
Conic sections
Analytic geometry
Curves
Celestial mechanics
Astrodynamics
Hyperbola
Ellipse
Semi-minor axis
Semi-major axis
Parabola

Analytical Geometry Final Review Courtesy of Your Friend: Daryll Mu?oz Formulas and Equations: Midpoint Formula of P(x1, y1), P?(x2, y2): Distance Formula of P(x1, y1), P?(x2, y2): Slope-Intercept Form y = mx + b Point-Slope Form y2 - y1 = m(x2 - x1) General Form of a Line Ax + By + C = 0 Standard Form of a Line Ax + By = C *Slope of line is (?A/B Slope of P(x1, y1), P?(x2, y2): *Slopes of parallel lines are equal *Slopes of perpendicular lines are opposite and reciprocal Directed Distance from line Ax+By+C=0 to point P(x1, y1) * The sign of the denominator is the same sign as ?B? in the line. *The directed distance will be positive if the point P is above the line, and negative if P is below the line. Directed Distance Between 2 Parallel Lines

Ellipses

Subject: 
Trigonometry
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geometry
Conic sections
Algebraic geometry
Ellipse
Semi-minor axis
Semi-major axis
focus
eccentricity
Circle
Line Segment
Hyperbola
Director circle

An ellipse is the set of points such that the sum of the distances from any point on the ellipse to two other fixed points is constant. The two fixed points are called the foci (plural of focus) of the ellipse. Figure %: The sum of the distances d1 + d2 is the same for any point on the ellipse. The line segment containing the foci of an ellipse with both endpoints on the ellipse is called the major axis. The endpoints of the major axis are called the vertices. The point halfway between the foci is the center of the ellipse. The line segment perpendicular to the major axis and passing through the center, with both endpoints on the ellipse, is the minor axis.

Conics

Subject: 
Trigonometry
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geometry
Algebraic geometry
Conic sections
Analytic geometry
Curves
Birational geometry
Parabola
Hyperbola
Ellipse
focus
Pole and polar
Euclidean geometry
conics

Analytic geometry is roughly the same as plane geometry except that in analytic geometry, figures are studied in the context of the coordinate plane. Instead of focusing on the congruence of shapes like plane geometry, analytic geometry deals with the coordinates of shapes and formulas for their graphs in the coordinate plane. Much of analytic geometry focuses on the conics. A conic is a two-dimensional figure created by the intersection of a plane and a right circular cone. All conics can be written in terms of the following equation: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 . The four conics we'll explore in this text are parabolas, ellipses, circles, and hyperbolas.
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