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CSM_Chapters10.pdf

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Chapter 10 Conics and Polar Coordinates 10.1 Conic Sections y x 1. vertex: (0, 0) focus: (1, 0) directrix: x = −1 axis: y = 0 y x 2. vertex: (0, 0) focus: (7/8, 0) directrix: x = − 7 8 axis: y = 0 y x 3. vertex: (0, 0) focus: (0, −4) directrix: y = 4 axis: x = 0 668 10.1. CONIC SECTIONS 669 y x 4. vertex: (0, 0) focus: _ 0, 1 40 _ directrix: y = − 1 40 axis: x = 0 y x 5. vertex: (0, 1) focus: (4, 1) directrix: x = −4 axis: y = 1 y
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  Chapter 10 Conics and Polar Coordinates 10.1 Conic Sections yx 1. vertex: (0 , 0)focus: (1 , 0)directrix:  x  = − 1axis:  y  = 0 yx 2. vertex: (0 , 0)focus: (7 / 8 , 0)directrix:  x  = − 78 axis:  y  = 0 y x 3. vertex: (0 , 0)focus: (0 , − 4)directrix:  y  = 4axis:  x  = 0668  10.1. CONIC SECTIONS   669 y x 4. vertex: (0 , 0)focus:  0 ,  140  directrix:  y  = −  140 axis:  x  = 0 y x 5. vertex: (0 , 1)focus: (4 , 1)directrix:  x  = − 4axis:  y  = 1 y x 6. vertex: ( − 2 , − 3)focus: ( − 4 , − 3)directrix:  x  = 0axis:  y  = − 3 yx 7. vertex: ( − 5 , − 1)focus: ( − 5 , 2)directrix:  y  = 0axis:  x  = − 5  670  CHAPTER 10. CONICS AND POLAR COORDINATES  yx 8. vertex: (2 , 0)focus:  2 , − 14  directrix:  y  =  14 axis:  x  = 2 y x 9. ( y  + 6) 2 = 4( x + 5)vertex: ( − 5 , − 6)focus: ( − 4 , − 6)directrix:  x  = − 6axis:  y  = − 6 y x 10. ( x + 3) 2 = − ( y  + 2)vertex: ( − 3 , − 2)focus: ( − 3 , − 9 / 4)directrix:  y  = − 7 / 4axis:  x  = − 3 yx 11.  x +  52  2 =  14 ( y − 1)vertex: ( − 5 / 2 , − 1)focus: ( − 5 / 2 , − 15 / 16)directrix:  y  = − 17 / 16axis:  x  = −− 5 / 2  10.1. CONIC SECTIONS   671 yx 12. ( x − 1) 2 = 4( y − 4)vertex: (1 , 4)focus: (1 , 5)directrix:  y  = 3axis:  x  = 1 y x 13. ( y − 4) 2 = − 2( x + 3)vertex: (3 , 4)focus: (5 / 2 , 4)directrix:  x  = 7 / 2axis:  y  = 4 yx 14. ( y − 2) 2 = 4  x +  14  vertex: ( − 1 / 4 , 2)focus: (3 / 4 , 2)directrix:  x  = − 5 / 4axis:  y  = 215.  x 2 = 2816.  y 2 = − 16 x 17.  y 2 = 10 x 18.  x 2 = − 40 y 19. The parabola is of the form ( y − k ) 2 = 4  p ( x − h ) with ( h,k ) = ( − 2 , − 7) and  p  = 3 .  Thus theequation is ( y  + 7) 2 = 12( x + 2) . 20. The parabola is of the form ( x − h ) 2 = 4  p ( y − 5) with ( h,k ) = (2 , 0) and  p  = 3, so the equationof the parabola is ( x − 2) 2 = 12 y.
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