CK-12-Pre-Calculus Concepts

9.2. Parabolas http://www.ck12.org Example A Identify the following conic, put it into graphing form and identify its vertex, fo ...

http://www.ck12.org Chapter 9. Conics The vertex must be halfway between the focus and the directrix. This places it at (4, 1). ...

9.2. Parabolas http://www.ck12.org y^2 − 4 y+ 12 x− 32 = 0 Answers: The vertex must lie directly between the focus and the dire ...

http://www.ck12.org Chapter 9. Conics 8.y^2 + 2 y− 8 x+ 33 = 0 9.x^2 − 8 x+ 20 y+ 36 = 0 10.x^2 + 6 x− 12 y− 15 = 0 11.y^2 − 12 ...

9.3. Circles http://www.ck12.org 9.3 Circles Here you will formalize the definition of a circle, translate a conic from standard ...

http://www.ck12.org Chapter 9. Conics Example B Turn the following equation into graphing form for a circle. Identify the center ...

9.3. Circles http://www.ck12.org Solution: The center of the circle is at (3, 1) and the radius of the circle isr=4. The equatio ...

http://www.ck12.org Chapter 9. Conics 2. x^2 − 34 x+y^2 + 24 y+^7492 = 0 x^2 − 34 x+y^2 + 24 y=−^7492 x^2 − 34 x+ 289 +y^2 + 24 ...

9.3. Circles http://www.ck12.org 12. 13. 14. ...

http://www.ck12.org Chapter 9. Conics 15. ...

9.4. Ellipses http://www.ck12.org 9.4 Ellipses Here you will translate ellipse equations from standard conic form to graphing fo ...

http://www.ck12.org Chapter 9. Conics The general equation for an ellipse is: (x−h)^2 a^2 + (y−k)^2 b^2 =^1 In this case the maj ...

9.4. Ellipses http://www.ck12.org The focal radius is 3. This means that the foci are at (3, 0) and (-3, 0). The eccentricity is ...

http://www.ck12.org Chapter 9. Conics Eccentricity is the ratio of the focal radius to the semi major axis: e=ca. Vocabulary The ...

9.4. Ellipses http://www.ck12.org 3. 9 x^2 − 9 x+ 4 y^2 + 12 y+^94 =− 8 9 x^2 − 9 x+^94 + 4 y^2 + 12 y=− 8 9 ( x^2 −x−^14 ) + 4 ...

http://www.ck12.org Chapter 9. Conics 9x^2 − 36 x+ 4 y^2 + 16 y+ 52 = 36 Find the equation for each ellipse based on the descri ...

9.5. Hyperbolas http://www.ck12.org 9.5 Hyperbolas Here you will translate conic equations into graphing form and graph hyperbol ...

http://www.ck12.org Chapter 9. Conics When graphing, the constantsaandbenable you to draw a rectangle around the center. The tra ...

9.5. Hyperbolas http://www.ck12.org Example B Find the equation of the hyperbola with foci at (-3, 5) and (9, 5) and asymptotes ...

http://www.ck12.org Chapter 9. Conics x^2 − 2 x+ 1 +(y− 2 )^2 =^94 (x^2 − 10 x+ 25 ) x^2 − 2 x+ 1 −^94 x^2 +^904 x−^2254 +(y− 2 ...