Conic Sections - Lines

1
Conic Sections - Lines

• General Equation
• y y1 m(x x1)
• M slope, (x1,y1) gives one point on this line.
• Standard Form
• ax by c
• Basic Algebra can be used to change the format of
  a line from point-slope (general equation) to
  standard form.
• Special Cases
• Parallel Lines Will have the same slope.
• Perpendicular Lines Will have a negative
  reciprocal slope. Ex one slope of 2/3 other
  slope of -3/2

2
Conic Sections Parabolas

• General Equation
• y y1 a(x-x1)2
• ONLY 1 VALUE CAN BE SQUARED IN A PARABOLA!
• (x1,y1) now gives turning point of the parabola.
• a value determines opening direction
• a value positive parabola opens up
• a value negative parabola opens down
• a value also determines parabola behavior
• a value is 1 parabola is normal
• a value stronger than 1 parabola is skinny
• a value fraction weaker than 1 parabola is wide

3
Conic Sections Parabolas Contd

• Other format for parabola
• y ax2 bx c
• formula x -b/(2a)
• Gives the x value of the parabolas turning point
• To find the y value of turning point, plug x
  value into equation
• Use x value of turning point to balance table on
  graphing calculator
• Graph points to model parabola

4
Conic Sections - Circles

• Both x and y must be squared!
• Anytime x and y are both squared, must be
  algebraically converted to equal to 1.
• General Equation
• (x x1)2 (y - y1)2 1
• a2 a2
• A and b must be the same number for a circle
• (x1,y1) gives the center point of the circle
• a value gives the radius of the circle

5
Conic Sections - Ellipses

• Both x and y must be squared!
• Anytime x and y are both squared, must be
  algebraically converted to equal to 1.
• General Equation
• (x x1)2 (y - y1)2 1
• a2 b2
• a and b must be the DIFFERENT numbers for an
  ellipse
• (x1,y1) gives the center point of the ellipse
• a value gives the x- radius / x-stretch of the
  ellipse
• b value gives the y-radius / y-stretch of the
  ellipse

6
Conic Sections - Hyperbolas

• Both x and y must be squared! MUST HAVE MINUS
  SIGN!!
• Anytime x and y are both squared, must be
  algebraically converted to equal to 1.
• General Equation Either x or y can come first.
• (x x1)2 - (y - y1)2 1
• a2 b2
• a and b can be the same or different, doesnt
  matter for hyperbola
• (x1,y1) gives the center point a and b still
  give Stretch values just like ellipse.
• Hyperbola breaks at stretch points, depending on
  formula.