Conic Sections PDF

CONIC SECTIONS ANALYTIC GEOMETRY   Conic Sections The general form of the equation of conic section is a quadratic equation given by: 𝟐 𝟐 𝑨𝒙 + 𝑩𝒚 + 𝑪𝒙 + 𝑫𝒚 + 𝑬 = 𝟎  Circle If A and B are equal, the equation may be that...

CONIC SECTIONS ANALYTIC GEOMETRY   Conic Sections The general form of the equation of conic section is a quadratic equation given by: 𝟐 𝟐 𝑨𝒙 + 𝑩𝒚 + 𝑪𝒙 + 𝑫𝒚 + 𝑬 = 𝟎  Circle If A and B are equal, the equation may be that of a circle. Examples 𝟐 𝟐 𝟒𝒙 + 𝟒𝒚 + 𝟖𝒙 + 𝟐𝟎𝒚 + 𝟏 = 𝟎  Ellipse If A and B are not equal but have the same signs, the equation may be that of an ellipse. Examples 𝟐 𝟐 𝟒𝒙 + 𝟓𝒚 + 𝟖𝒙 − 𝟐𝟎𝒚 − 𝟏𝟓 = 𝟎  Hyperbola If A and B have opposite signs, the equation maybe that of a hyperbola Examples 𝟐 𝟐 −𝟒𝒙 + 𝒚 + 𝒙 + 𝟏𝟓𝒚 − 𝟐𝟏 = 𝟎  Parabola If A = 0 or B = 0 but not both, the equation may be that of a parabola. Examples 𝟐 𝟏𝟑𝒙 + 𝟖𝒙 − 𝟏𝟏𝒚 + 𝟏𝟓 = 𝟎 LET’s Try Identify the type of conic sections of the following equations. THIS! 𝟐 𝟐 𝒙 + 𝟔𝒙 + 𝒚 − 𝟖𝒚 + 𝟗 = 𝟎 𝟐 𝟐 𝒙 − 𝒚 = 𝟏𝟔 𝟐 𝟐 𝟑𝒙 + 𝒚 − 𝟒𝒙 + 𝟔𝒚 − 𝟏𝟐 = 𝟎 𝟐 𝟐 𝟒𝒙 + 𝟗𝒚 = 𝟑𝟔 LET’s Try Identify the type of conic sections of the following equations. THIS! 𝟐 𝒙 − 𝟒𝒚 + 𝟖 = 𝟎 𝟐 𝟐 𝒙 + 𝟐𝒙 + 𝒚 − 𝟑 = 𝟎 𝟐 𝟒𝒙 − 𝟖𝒙 + 𝟏𝟔𝒚 − 𝟏𝟐 = 𝟎 𝟐 𝟐 𝟐𝒙 − 𝟖𝒚 − 𝟏𝟔𝒚 − 𝟏𝟔 = 𝟎