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

Conic Sections – Parabolas General Equation: y – y1 = a(x-x1) 2 ONLY 1 VALUE CAN BE SQUARED IN A PARABOLA! (x 1,y 1 ) 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

Conic Sections – Parabolas – Cont’d Other format for parabola: y = ax 2 + bx + c formula x = -b/(2a) – Gives the x value of the parabola’s 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

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 – x 1 ) 2 + (y - y 1 ) 2 = 1 a 2 a 2 A and b must be the same number for a circle (x 1,y 1 ) gives the center point of the circle “a” value gives the radius of the circle

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 – x 1 ) 2 + (y - y 1 ) 2 = 1 a 2 b 2 a and b must be the DIFFERENT numbers for an ellipse (x 1,y 1 ) 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

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 – x 1 ) 2 - (y - y 1 ) 2 = 1 a 2 b 2 a and b can be the same or different, doesn’t matter for hyperbola (x 1,y 1 ) gives the center point – a and b still give “Stretch values” just like ellipse. Hyperbola breaks at stretch points, depending on formula.