CONIC SECTIONS TEST FRIDAY, JANUARY 5 TH

Transcription

1 CONIC SECTIONS TEST FRIDAY, JANUARY 5 TH

2 DAY 1 - CLASSIFYING CONICS 4 Conics Parabola Circle Ellipse Hyperbola

3 DAY 1 - CLASSIFYING CONICS GRAPHICALLY Parabola Ellipse Circle Hyperbola

4 DAY 1 - CLASSIFYING CONICS IN STANDARD FORM Parabola y = a x h 2 + k x = a y k 2 + h Ellipse x h 2 a 2 + x h 2 b 2 + y k 2 b 2 = 1 2 y k a 2 = 1 Circle x h 2 + y k 2 = r 2 Hyperbola x h 2 y k 2 a 2 b 2 = 1 y k 2 a 2 x h 2 b 2 = 1

5 DAY 1 - CLASSIFYING CONICS x = 1 16 y x y = 1 x y = 1 x y 2 2 = 27

6 DAY 1 - CLASSIFYING CONICS IN POLYNOMIAL FORM (SET = 0) Parabola One Squared Term Ellipse Two Squared Terms Same Sign Different Coefficients Circle Special Case of the Ellipse Two Squared Terms Same Sign Same Coefficients Hyperbola Two Squared Terms Opposite Signs Any Coefficient Same or Different it is still a Hyperbola

7 DAY 1 - CLASSIFYING CONICS 4x 2-9x + y 5 = 0 4x 2 - y 2 + 8x - 6y + 4 = 0 2x 2 = - 4y 2 + 4x - 12y 2x 2-8x + 2 = - 2y 2-12y x 2 + 6x = y 5 y 2 + 2x = 9 + 2x 2 2y 8x = 5y 2 16x + 28y 2x 2 + 3y = 2y 2 + 5x + 5 9x = 25y x + 50y 16x x = 9y 2 144y 496 Parabola Hyperbola Ellipse Circle Parabola Hyperbola Ellipse Circle Ellipse Hyperbola

8 DAY 1 - GRAPHING CONIC SECTIONS Parabolas Vertex: (h, k) Focus: (h, k + p) (h + p, k) Directrix: y = k p x = h p Focal Length: p Focal Width: 4p y = 1 4p x h 2 + k x = 1 4p y k 2 + h *When graphing a parabola, the squared term defines the direction the parabola opens. a > 0 a < 0 x 2 UP DOWN y 2 RIGHT LEFT x = 1 2 y Vertex: (3, 2) p-value: 1 2 Focus: 5 2, 2 Directrix: x = 7 2

9 SATELLITE/PARABOLIC DISHES

10 NCSU WHISPER DISHES

11 DAY 1 - GRAPHING CONIC SECTIONS x = 1 16 y

12 HOMEWORK (DAY 1) Complete Kuta #1-22 classification and justification!!! P. 701 #1-6 all, #7-17 odd Quiz Wednesday, December 20

13 WARM-UP (DAY 2) Classify each of the following. 1) 2x 2 3x + 4y = 7 2) 4x 2 5x + 4y 2 5y = 20 3) 3x 2 + 2x = 3y 2 2y 4) 10x 2 + 9x + 8y 2 + 7y + 6 = 0

14 DAY 2 - POLYNOMIAL TO STANDARD FORM Write the standard form of the conic. If applicable, list the center, vertices, focus, directrix, and eccentricity of the conic. Then sketch the conic. 6x y 2 4y = 22

15 DAY 2 - POLYNOMIAL TO STANDARD FORM Write the standard form of the conic. If applicable, list the center, vertices, focus, directrix, and eccentricity of the conic. Then sketch the conic. 3x 2 12x y = 0

16 DAY 2 - POLYNOMIAL TO STANDARD FORM Write the standard form of the conic. If applicable, list the center, vertices, focus, directrix, and eccentricity of the conic. Then sketch the conic. 1 2 y2 4y + 8x 8 = 0

17 HOMEWORK (DAY 2) P. 701 #19-24 all Quiz Wednesday, December 20

18 DAY 3 - GRAPHING CONIC SECTIONS Circles x h 2 + y k 2 = r 2 Center: (h, k) Radius: r Eccentricity: 0 = c a Center: (3, 2) x y = 16 Radius: 16 = 4

19 DAY 3 - GRAPHING CONIC SECTIONS x y 2 2 = 27

20 DAY 3 - GRAPHING CONIC SECTIONS Ellipses Center: (h, k) Major Axis: 2a Minor Axis: 2b Foci: c 2 = a 2 b 2 Eccentricity: 0 < c a < 1 x+1 2 x h 2 a 2 + x h 2 b y k b 2 = 1 y k 2 a 2 = 1 *When graphing an ellipse, a > b. If a is under the x value, then the graph has a horizontal major axis. If a is under the y value, then the graph has a vertical major axis. Center: ( 1, 2) 25 + y = 1 Major Axis: 10 (horizontal) Minor Axis: 4 (vertical) Foci: ( 1 ± 21, 2) Eccentricity:

21 DAY 3 - GRAPHING CONIC SECTIONS x y = 1

22 US CAPITOL WHISPER MYTH

23 DAY 3 - POLYNOMIAL TO STANDARD FORM Write the standard form of the conic. If applicable, list the center, vertices, co-vertices, focus, directrix, name the axis (find the length), and eccentricity of the conic. Then sketch the conic. 4x 2 + 4y 2 24x + 40y 60 = 0

24 DAY 3 - POLYNOMIAL TO STANDARD FORM Write the standard form of the conic. If applicable, list the center, vertices, co-vertices, focus, directrix, name the axis (find the length), and eccentricity of the conic. Then sketch the conic. 9x y 2 36x 50y 164 = 0

25 HOMEWORK (DAY 3) P. 710 #1-22 all Quiz Wednesday, December 20

26 WARM-UP (DAY 4) Sketch: y x = 1

27 DAY 4 - GRAPHING CONIC SECTIONS Hyperbolas Center: (h, k) Transverse Axis: 2a Conjugate Axis: 2b Foci: c 2 = a 2 + b 2 Asymptotes: y k = ±m(x h) Center: ( 1, 2) Transverse Axis: 6 (vertical) Conjugate Axis: 2 (horizontal) Foci: 1, 2 ± 10 Asymptotes: y 2 = ±3(x + 1) x h 2 2 y k a 2 b 2 = 1 y k 2 a 2 x h 2 b 2 = 1 y x = 1 *If a is under the x value, then the graph has a horizontal transverse axis. If a is under the y value, then the graph has a vertical transverse axis.

28 DAY 4 - GRAPHING CONIC SECTIONS x y = 1

29 DAY 4 - POLYNOMIAL TO STANDARD FORM Write the standard form of the conic. If applicable, list the center, vertices, co-vertices, focus, directrix, name the axis (find the length) and eccentricity of the conic. Then sketch the conic. 16y 2 x 2 + 2x + 64y + 54 = 0

30 HOMEWORK (DAY 4) P. 720 #1-22 all Quiz Wednesday, December 20

31 WARM-UP (DAY 5) Sketch and label all the key information: Partner A: 4x 2 + 9y 2 32x 90y = 0 Partner B: 4y 2 x 2 + 6x 24y + 11 = 0

32 PRACTICE (DAY 5) Sketch and label all the key information: 3y 2 x 2y + 1 = 0

33 DAY 5 - WRITING THE EQUATION OF A PARABOLA Find the standard form of the equation of the conic with the following information: 1) Vertex: ( 1, 2) Focus: ( 1, 0) 2) Vertex: 2, 1 Directrix: x = 1 3) Focus: (4, 12) Directrix: x = 8 4) Vertex: (5, 3) Through the point: (4. 5, 4)

34 DAY 5 - WRITING THE EQUATION OF A ELLIPSE Find the standard form of the equation of the conic with the following information: 1) Vertices: 2, 6 & (2, 0) Co-vertices: 1, 3 & (3, 3) 2) Center: (2, 1) Vertex: 2, 1 2 Minor axis length: 2 3) Center: (3, 2) a = 3c Foci: 1, 2

35 DAY 5 - WRITING THE EQUATION OF A HYPERBOLA Find the standard form of the equation of the conic with the following information: 1) Vertices: (0, ±2) Foci: (0, ±5) 2) Foci: (±10, 0) Asymptotes: y = ± 3 4 x 3) Vertices: ±2, 1 Passing through: (5, 4)

36 HOMEWORK (DAY 5) P. 702 #41-47 odd P. 711 #35-47 odd P. 720 #23-33 odd Quiz Tomorrow, December 20

37 AFTER THE QUIZ Start on Test Review Part #1 Answers posted online. When we return Test Friday, January 5 th