1. Conic sections
Review

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

3. 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

4. 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

5. 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

6. classwork
Page 253, 3,4, 6-10

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

8. 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 = 𝑥+ 𝑏 2 2
+9+4

9. 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

10. 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:

11. 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.

12. 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.

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

14. 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)

15. 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