10.6 - Identifying Conic Sections Worksheet Key 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Worksheet Key 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Recall Equations of Conics: Put the equations in standard form 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Quick Examples Identify whether it is a circle, ellipse, hyperbola, or parabola? 1. 2. 3. 4. c i r c l e e l l i p s e p a r a b o l a h y p e r b o l a 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

Steps in Identifying Conics Put the standard form equation in coefficient ABC order, Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. Identify A, B, and C Apply the discriminant formula, b2 – 4ac Determine the answer to identify the proper conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

Classifying Conic Sections All conic sections can be written in the general form Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. Circles and Ellipses using b2 – 4ac Circles b2 – 4ac < 0 b = 0 AND a = c Ellipses b ≠ 0 OR a ≠ c 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

Classifying Conic Sections All conic sections can be written in the general form Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. Parabolas and Hyperbolas using b2 – 4ac Parabolas b2 – 4ac = 0 Hyperbolas b2 – 4ac > 0 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 1 Identify the conic section that the equation represents and the discriminant, 12x2 + 24xy + 12y2 + 25y = 0 and show all work A. Put the standard form equation in coefficient ABC order, Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. 12x2 + 24xy + 12y2 + 25y = 0 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 1 Identify the conic section that the equation represents and the discriminant, 12x2 + 24xy + 12y2 + 25y = 0 and show all work B. Put in A, B, and C 12x2 + 24xy + 12y2 + 25y = 0 A = 12, B = 24, C = 12 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 1 Identify the conic section that the equation represents and the discriminant, 12x2 + 24xy + 12y2 + 25y = 0 and show all work C. Apply the discriminant formula, b2 – 4ac A = 12, B = 24, C = 12 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 1 Identify the conic section that the equation represents and the discriminant, 12x2 + 24xy + 12y2 + 25y = 0 and show all work D. Determine the answer to identify the proper conic Circles b2 – 4ac < 0 b = 0 AND a = c Ellipses b ≠ 0 OR a ≠ c Parabolas b2 – 4ac = 0 Hyperbolas b2 – 4ac > 0 A = 12, B = 24, C = 12 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 2 Identify the conic section that the equation represents and discriminant, 9x2 + 9y2 – 18x – 12y – 50 = 0 and show all work 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 3 Identify the conic section that the equation represents and the discriminant, 8x2 – 15xy + 6y2 + x – 8y + 12 = 0 and show all work 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Your Turn Identify the conic section that the equation represents and the discriminant, 4x2 + y2 = 8x + 8 and show all work 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

Steps in Completing the Square Identify whether it is an ellipse by using the equation, b2 – 4ac where the answer is less than zero using the equation, Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 Rearrange variables for x’s and y’s through factoring Take GCF and add everything to other side Use completing the square; using what’s added to the x’s and y’s is added to the radius Identify the coefficient which is raised to the first power and divide the term by 2 Take the second term, divide the term by 2, and square that number Add to both sides to the equation Put the equation into factored form Put it in standard form 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 4 Change the equation x2 + y2 + 8x – 6y – 11 = 0 to standard form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 4 Change the equation x2 + y2 + 8x – 6y – 11 = 0 to standard form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 4 Change the equation x2 + y2 + 8x – 6y – 11 = 0 to standard form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 5 Change the equation x2 + 4y2 + 10x – 8y + 13 = 0 to standard form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 5 Change the equation x2 + 4y2 + 10x – 8y + 13 = 0 to standard form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 5 Change the equation x2 + 4y2 + 10x – 8y + 13 = 0 to standard form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 5 Change the equation x2 + 4y2 + 10x – 8y + 13 = 0 to standard form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 6 Change the equation 16x2 – 9y2 – 64x + 18y – 89 = 0 to standard form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 7 Change the equation x2 + 14x – 12y + 97 = 0 to standard form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Your Turn Change the equation –4x2 + 16y2 – 16x + 32y – 64 = 0 to standard form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 8 Change the equation (x – 1)2 + (y + 2)2 = 4 to general form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 9 Change the equation to general form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 9 Change the equation to general form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Example 10 Change the equation 9x = (y + 8)2 to general form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Your Turn Change the equation to general form and identify the conic 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections

10.6 - Identifying Conic Sections Assignment Worksheet 2/22/2019 1:55 PM 10.6 - Identifying Conic Sections