Conic sections Review

agenda Homework Q and A Team test expectations Resources and extra help suggestions Test review

Team test expectations for next class Choose a team of 2, 3, or 4. Each person in the team will complete the work on their own Quiz paper You may use all of your notes You may not use a book You may not use your phone You may not ask for help from students on different teams The posters will not be available for you to look at

Team test grading You will staple your team papers together as a packet and turn it in. I will pick one paper in the packet to grade. That grade will be the grade for the whole team. Grading, like all tests will be based on accuracy You must show your work, when requested, to get full credit The team test is worth 35 points in the assessment category

Additional resources On my blog: jyoung1math.wordpress.com , I’ve posted this powerpoint with the graphs and formulas for our four basic shapes. Read your Book

classwork Page 253, 3,4, 6-10

Conic Section – A figure formed by the intersection of a plane and a right circular cone

6.2 Equations of Circles +9+4 Completing the square when a=1 Circle with radius r & center (0,0) Completing the square when a=1 𝑥 2 +𝑏𝑥+ 𝑏 2 2 = 𝑥+ 𝑏 2 2 +9+4

The Standard Form of the Equation of the Ellipse The standard form of an ellipse centered at the origin with the major axis of length 2a along the x-axis and a minor axis of length 2b along the y-axis, is: The standard form of an ellipse centered at the origin with the major axis of length 2a along the y-axis and a minor axis of length 2b along the x-axis, is: vertex 𝑭 𝟏 (0,c) vertex 𝑭 𝟏 𝑭 𝟐 vertex 𝑭 𝟐 (0,-c) vertex 𝑐 2 = 𝑎 2 − 𝑏 2 𝑐 2 = 𝑎 2 − 𝑏 2

The Standard Form of the Equation of the Ellipse The standard form of an ellipse centered at any point (h, k) with the major axis of length 2a parallel to the y-axis and a minor axis of length 2b parallel to the x-axis, is: The standard form of an ellipse centered at any point (h, k) with the major axis of length 2a parallel to the x-axis and a minor axis of length 2b parallel to the y-axis, is: (h, k) (h, k) 𝑐 2 = 𝑎 2 − 𝑏 2 𝑐 2 = 𝑎 2 − 𝑏 2 Foci: Foci:

To find the foci use c2 = a2 + b2 The Standard Equation of a Hyperbola With Center (0, 0) and Foci on the x-axis Horizontal Hyperbola The equation of a hyperbola with the center (0, 0) and foci on the x-axis is: 𝐁 𝟏 (0, b) The length of the rectangle is 2a. The height of the rectangle is 2b. The vertices are (a, 0) and (-a, 0). The foci are (c, 0) and (-c, 0). The slopes of the asymptotes are (-c, 0) A1 A2 (c, 0) F1 (-a, 0) (a, 0) F2 𝐁 𝟐 (0, -b) To find the foci use c2 = a2 + b2 The equations of the asymptotes are 𝒚= 𝒃 𝒂 𝒙 and 𝒚=− 𝒃 𝒂 𝒙.

The equations of the asymptotes are 𝒚= 𝒂 𝒃 𝒙 and 𝒚=− 𝒂 𝒃 𝒙. The Standard Equation of a Hyperbola with Center (0, 0) and Foci on the y-axis Vertical Hyperbola The equation of a hyperbola with the center (0, 0) and foci on the y-axis is: F1(0, c) A1(0, a) The length of the rectangle is 2b. The height of the rectangle is 2a. The vertices are (0, a) and (0, -a). The foci are (0, c) and (0, -c). The slopes of the asymptotes are B1(-b, 0) B2(b, 0) To find the foci use c2 = a2 + b2 A2(0, -a) F2(0, -c) The equations of the asymptotes are 𝒚= 𝒂 𝒃 𝒙 and 𝒚=− 𝒂 𝒃 𝒙.

𝑐 2 = 𝑎 2 − 𝑏 2 𝑐 2 = 𝑎 2 − 𝑏 2 Foci: Foci:

Parabola Equation center at the origin (0,0) 𝒑= 𝟏 𝟒𝒂 𝒂= 𝟏 𝟒𝒑 𝒐𝒓 − 𝟏 𝟒𝒑 𝟒. 𝒙=− 𝟏 𝟒𝒑 𝒚 𝟐 𝟏. 𝒚= 𝟏 𝟒𝒑 𝒙 𝟐 𝟐. 𝒚=− 𝟏 𝟒𝒑 𝒙 𝟐 𝟑. 𝒙= 𝟏 𝟒𝒑 𝒚 𝟐 p p p p p (p, 0) p p)

Parabola Equation center at (h,k) 𝒚= 𝟏 𝟒𝒑 𝒙−𝒉 𝟐 +𝒌 𝒚=− 𝟏 𝟒𝒑 𝒙−𝒉 𝟐 +𝒌 𝒙= 𝟏 𝟒𝒑 𝒚−𝒌 𝟐 +𝒉 𝒙=− 𝟏 𝟒𝒑 𝒚−𝒌 𝟐 +𝒉