Work on the first page of today’s packet.

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Work on the first page of today’s packet. assignment, pencil, red pen, highlighter, notebook, calculator U5D3 Have out: Bellwork: Work on the first page of today’s packet. Match the equation of the ellipse its graph, then graph the two ellipses at the bottom of the worksheet. Be sure to find the coordinates of the foci.

2 1 6 3 5 4

II. Graph each ellipse. Identify the coordinates for the center, the foci, and the endpoints of the major and minor axes. y 10 x –10 (0,6) 1) Center: (0, 0) (–3,0) (3,0) major axis: Y, vertical ellipse a = 6 c2 = a2 – b2 b = 3 c2 = 62 – 32 c = 5.20 c2 = 36 – 9 (0,–6) foci: (0, ±5.20) c2 = 27 c ≈ 5.20

II. Graph each ellipse. Identify the coordinates for the center, the foci, and the endpoints of the major and minor axes. x y 10 –10 (–3, 9) 2) (–10,4) (4,4) Center: (–3, 4) major axis: X, horizontal ellipse a = 7 (–3,–1) b = 5 c2 = a2 – b2 c = 4.90 c2 = 72 – 52 foci: (–3 ± 4.90, 4) c2 = 49 – 25 (–7.90, 4) c2 = 24 (1.90, 4) c ≈ 4.90

III. Write the standard form equation of an ellipse. group x’s and y’s + 8 + 8 get constants to one side factor coefficients from the variables 4 1 4 4(1) then complete the square 1 1 Divide to put equation in STANDARD form. 16 16 16 4 1

III. Write the standard form equation of an ellipse. b) group x’s and y’s get constants to one side factor coefficients from the variables 1 25(1) then complete the square 1 1 1 Divide to put equation in STANDARD form. 1 2025 2025 2025 25 81 Try c & d on your own.

Circles vs. Ellipses: How do you tell the difference between their general equations? x2 , y2, different coefficients, but positive x2 , y2, same positive coefficients Circle: ___________________ Ellipse: ___________________ IV. Decide whether the graph of each equation is a circle or an ellipse. Write the equation in standard form. a) Circle! coefficients are the same 25 25 center: (0, –5) r = 3

Ellipse! coefficients are different d) V. Decide whether the graph of each equation is a circle or an ellipse. Write the equation in standard form. Ellipse! coefficients are different d) 16 4 64 100 Remember ellipses in standard form = 1 1 1 1 25 4 1 Horizontal a = 5 Center: (4, –2) b = 2 Foci: (8.58, –2) (–0.58, –2) c =

Finish the worksheets

Finish parts d – f on your own. III. Write the standard form equation of an ellipse. c) group x’s and y’s get constants to one side factor 4 from the y’s 4 9 4 4(9) then complete the square 1 1 Divide to put equation in STANDARD form. 16 16 16 4 1 Finish parts d – f on your own.