1 / 12

4( x 2 – 2 x + ? ) + y 2 = 8 + 4( ? )

Note that A = 4, B = 0, and C = 1 , so the value of the discriminant is:. B 2 – 4 AC = 0 2 – 4(4)(1) = –16. Because B 2 – 4 AC < 0 and A = C, the conic is an ellipse. To graph the ellipse, first complete the square in x. EXAMPLE 6. Classify a conic.

Télécharger la présentation

4( x 2 – 2 x + ? ) + y 2 = 8 + 4( ? )

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Note thatA = 4, B = 0,andC = 1, so the value of the discriminant is: B2 – 4AC = 02 – 4(4)(1) = –16 BecauseB2– 4AC < 0andA = C, the conic is an ellipse. To graph the ellipse, first complete the square in x. EXAMPLE 6 Classify a conic Classify the conic given by4x2 + y2 – 8x – 8 = 0. Then graph the equation. SOLUTION 4x2 + y2 – 8x – 8 = 0 (4x2 – 8x) + y2 = 8 4(x2 – 2x) + y2 = 8 4(x2– 2x + ? ) + y2 = 8 + 4( ? )

  2. (x – 1)2 y2 12 + = 1 3 From the equation, you can see that(h, k) = (1, 0), a = 12 = 2 3 ,andb = 3. Use these facts to draw the ellipse. EXAMPLE 6 Classify a conic 4(x2– 2x + 1) + y2 = 8 + 4(1) 4(x – 1)2 + y2 = 12

  3. EXAMPLE 7 Solve a multi-step problem Physical Science In a lab experiment, you record images of a steel ball rolling past a magnet. The equation 16x2 – 9y2 – 96x + 36y – 36 = 0 models the ball’s path. • What is the shape of the path? • Write an equation for the path in standard form. • Graph the equation of the path.

  4. EXAMPLE 7 Solve a multi-step problem SOLUTION STEP 1 Identify the shape. The equation is a general second-degree equation withA = 16, B = 0,andC = –9. Find the value of the discriminant. B2 – 4AC = 02 – 4(16)(–9) = 576 BecauseB2 – 4AC > 0, the shape of the path is a hyperbola.

  5. (x – 3)2 9 (y –2)216 – = 1 EXAMPLE 7 Solve a multi-step problem STEP 2 Write an equation. To write an equation of the hyperbola, complete the square in both xand ysimultaneously. 16x2 – 9y2 – 96x + 36y – 36 = 0 (16x2 – 96x) – (9y2 – 36y) = 36 16(x2– 6x + ? ) – 9(y2– 4y + ? ) = 36 + 16( ? ) – 9(?) 16(x2– 6x + 9) – 9(y2– 4y + 4) = 36 + 16(9) – 9(4) 16(x – 3)2 – 9(y – 2)2 = 144

  6. Graph the equation. From the equation, the transverse axis is horizontal, (h, k) = (3, 2), a = 9 = 3 andb = 16. = 4 EXAMPLE 7 Solve a multi-step problem STEP 3 The vertices are at(3 +a, 2),or(6, 2)and(0, 2).

  7. EXAMPLE 7 Solve a multi-step problem STEP 3 Plot the center and vertices. Then draw a rectangle 2a = 6 units wide and 2b = 8 units high centered at (3, 2), draw the asymptotes, and draw the hyperbola. Notice that the path of the ball is modeled by just the right-hand branch of the hyperbola.

  8. for Examples 6 and 7 GUIDED PRACTICE 10. Classify the conic given byx2 + y2 – 2x + 4y + 1 = 0. Then graph the equation. ANSWER (x – 1)2 +( y + 2)2 = 4

  9. + y2 = 1 (x – 1)2 6 3 for Examples 6 and 7 GUIDED PRACTICE 11. Classify the conic given by2x2 + y2 – 4x – 4= 0. Then graph the equation. ANSWER Circle

  10. for Examples 6 and 7 GUIDED PRACTICE 12. Classify the conic given byy2 – 4y2 – 2x + 6= 0. Then graph the equation. ANSWER Parabola (y – 2)2 = 2(x –1)

  11. (x –2)2 (y +2)2 = 1 4 16 for Examples 6 and 7 GUIDED PRACTICE 13. Classify the conic given by4x2 – y2 – 16x –4y – 4= 0. Then graph the equation. ANSWER Hyperbola

  12. y2 – = 1 4 4(x – 1.5)2 4 for Examples 6 and 7 GUIDED PRACTICE 14. Astronomy An asteroid’s path is modeled by 4x2 + 6.25y2 – 12x –16 = 0 where x and y are in astronomical units from the sun. Classify the path and write its equation in standard form. Then graph the equation. ANSWER Hyperbola

More Related