Clearly here we also see that we can expect the value of to be between 0 and 1 Just like a parabola, the ellipse has a special reflective property. The reflective property of an Ellipse: of a line leaves one focus and hits the inside of the ellipse, it is reflected to hit the other focus … *** Make sure in Question 7 and 8, you get to the correct form. As an example, for question 7, the text book gives an answer of and just flippantly says, this is a Ellipse, but I need you to put it in the Ellipse form to show that it is an Ellipse … Chapter 9D Hyperbolas The Hyperbola equation has a similar form to Ellipses, but rather than adding the two and terms together, one is subtracted from the other. You may be used to Maths B Hyperbola where the asymptotes are horizontal and vertical. but in Maths C, the look like or they can be rotated by 90 degrees also. Hyperbola’s big “’s”, Where Ellipses have a major axis, have a transverse axis. (a line that contains the centre, foci Hyperbola’s and vertices). Similar to the minor axis of an Ellipse, the Hyperbola has a Conjugate Axis, and this is at a normal to the transverse axis and passes through the centre. The form of the Hyperbola graph, that is the Loci of a Hyperbola, are governed by the Same rule as the Parabola, , however here the Eccentricity of a Hyperbola is, , (in a parabola, ). In a Hyperbola the rule to find the Eccentricity is: Firstly, lets look at horizontal and vertical Hyperbolas. That is, where the transverse axis is either horizontal, or vertical. Horizontal Transverse axis: Vertical Transverse axis:
Clearly here we also see that we can expect the value of to be between 0 and 1 Just like a parabola, the ellipse has a special reflective property. The reflective property of an Ellipse: of a line leaves one focus and hits the inside of the ellipse, it is reflected to hit the other focus … *** Make sure in Question 7 and 8, you get to the correct form. As an example, for question 7, the text book gives an answer of and just flippantly says, this is a Ellipse, but I need you to put it in the Ellipse form to show that it is an Ellipse … Chapter 9D Hyperbolas The Hyperbola equation has a similar form to Ellipses, but rather than adding the two and terms together, one is subtracted from the other. You may be used to Maths B Hyperbola where the asymptotes are horizontal and vertical. but in Maths C, the Hyperbola’s look like big “’s”, or they can be rotated by 90 degrees also. Where Ellipses have a major axis, Hyperbola’s have a transverse axis. (a line that contains the centre, foci and vertices). Similar to the minor axis of an Ellipse, the Hyperbola has a Conjugate Axis, and this is at a normal to the transverse axis and passes through the centre. The form of the Hyperbola graph, that is the Loci of a Hyperbola, are governed by the Same rule as the Parabola, , however here the Eccentricity of a Hyperbola is, , (in a parabola, ). In a Hyperbola the rule to find the Eccentricity is: Firstly, lets look at horizontal and vertical Hyperbolas. That is, where the transverse axis is either horizontal, or vertical. Horizontal Transverse axis: Vertical Transverse axis:
12mc_conics_workbook.docx