Midterm Reviewer  Pre Calculus
LESSON 1: Conic Section (Conics) 



Conic Sections  Coefficient 

Circle  A = C ≠ 0 
Parabola  AC = 0 
Ellipse  AC > 0 
Hyberbola  AC < 0 
Examples:


Arc  Is a portion of the circumference Chord  A chord connects 2 points on the circle. A Line Segment, a line has no boundaries. It ends at 2 points on the circle. Diameter  A diameter is a chord because it connects 2 points in the circle. It is called the longest circle, the difference between the diameter and chord is that the diameter passes through the center. Radius  Is the distance from the center of the circle to any point on its circumference. Usually denoted by "R" or "r". Half the diameter. Secant Line  A straight line that intersects a circle in two points Tangent Line  A line that touches the circle at a single point. Sector  A portion of the area of the circle. The region bounded by an arc of the circle to the two radii to the arc’s endpoint 

A circle with its center at the origin, (0,0) and radius r has an equation,
A circle with its center at (h, k) and radius r has an equation,
Examples:
LESSON 2 : CONIC SECTIONS: PARABOLA 

Focus = (h, k + c) Directrix = y = k  c
Axis of symmetry = X = h 4c = C/4 2c = 2(C)
Endpoints:
Lr1 = (h + 2c, k + c)
Lr2 = (h  2c, k + c)
4c = the length of the latus rectum c = the distance from the vertex to the focus and from the vertex to the directrix 2c = the distance from the focus to the endpoints of the latus rectum 

Examples:
LESSON 3: CONIC SECTIONS: ELLIPSE 

Center: 0,0 Equation: Corresponding Graph: 

Center: 0,0 Equation: Corresponding Graph: 
Center: (h,k) Equation: Corresponding Graph: 
Center: (h,k) Equation: Corresponding Graph:

Examples:
LESSON 4: CONIC SECTIONS: HYPERBOLA 

LESSON 1: Conic Section (Conics) 



Conic Sections  Coefficient 

Circle  A = C ≠ 0 
Parabola  AC = 0 
Ellipse  AC > 0 
Hyberbola  AC < 0 
Examples:


Arc  Is a portion of the circumference Chord  A chord connects 2 points on the circle. A Line Segment, a line has no boundaries. It ends at 2 points on the circle. Diameter  A diameter is a chord because it connects 2 points in the circle. It is called the longest circle, the difference between the diameter and chord is that the diameter passes through the center. Radius  Is the distance from the center of the circle to any point on its circumference. Usually denoted by "R" or "r". Half the diameter. Secant Line  A straight line that intersects a circle in two points Tangent Line  A line that touches the circle at a single point. Sector  A portion of the area of the circle. The region bounded by an arc of the circle to the two radii to the arc’s endpoint 

A circle with its center at the origin, (0,0) and radius r has an equation,
A circle with its center at (h, k) and radius r has an equation,
Examples:
LESSON 2 : CONIC SECTIONS: PARABOLA 

Focus = (h, k + c) Directrix = y = k  c
Axis of symmetry = X = h 4c = C/4 2c = 2(C)
Endpoints:
Lr1 = (h + 2c, k + c)
Lr2 = (h  2c, k + c)
4c = the length of the latus rectum c = the distance from the vertex to the focus and from the vertex to the directrix 2c = the distance from the focus to the endpoints of the latus rectum 

Examples:
LESSON 3: CONIC SECTIONS: ELLIPSE 

Center: 0,0 Equation: Corresponding Graph: 

Center: 0,0 Equation: Corresponding Graph: 
Center: (h,k) Equation: Corresponding Graph: 
Center: (h,k) Equation: Corresponding Graph:

Examples:
LESSON 4: CONIC SECTIONS: HYPERBOLA 
