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!• (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

Conic Sections – Parabolas – Cont’d

• Other format for parabola:• y = ax2 + 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 – 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

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

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, doesn’t 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.