Algebra II Pre AP
Conics Review Worksheet
Name________________________
Date______________ Period_____
Identify the conic and write each of the following in standard form.
____
___________________________________ 1. x 2  y 2  4 x  16  0
____
___________________________________ 2. x 2  y 2  2 x  10 y  10  0
____
___________________________________ 3. 4 x2  y 2  24 x  4 y  36  0
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___________________________________ 4. x2  9 y 2  36 y  27  0
Omit
5. y 2  4 x  6 y  9  0
Omit
6. x 2  8x  2 y  16  0
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___________________________________ 7. x 2  4 y 2  8 y  8  0
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___________________________________ 8. x 2  9 y 2  6 x  0
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___________________________________ 9. 9 x2  4 y 2  36 x  8 y  4  0
____
___________________________________ 10. 16 x2  9 y 2  32 x  54 y  209  0
Write each of the following in standard form then find all appropriate information.
11. 4 x2  9 y 2  8x  36 y  4  0
12. 2 x2  y 2  20 x  8 y  50  0
center ___________
center ___________
endpts of major axis _____________________
vertices _____________________
endpts of minor axis _____________________
endpts of conjugate axis _______________
foci ____________________________
foci ____________________________
endpts of latus rectum ____________________
equations of asymptotes _______________
eccentricity ___________
eccentricity ___________
13. x2  y 2  4 x  9 y  1  0
14. y 2  x  2 y  8  0 OMIT
center _______________
vertex ___________ focus ____________
radius _______________
equation of directrix __________
equation of axis of symmetry ____________
endpts of latus rectum _________________
Using the following information, write an equation in standard form. Show all work.
_________________________ 15. Endpoints of diameter 1, 2  and  6, 12 
_________________________ 16. Circle with center on the x axis and tangent to the line y  3x  4 at  6, 22 
_________________________ 17. Circle with center in the first quadrant on the line x  4 and tangent to both axes
_________________________ 18. Circle with center at  6, 9  and tangent to the circle x2  y 2  4 x  6 y  12  0
_________________________ 19. Ellipse foci
 3, 2  and  3,
11 and sum of focal radii is 16
_________________________ 20. Ellipse tangent to the x and y axis and the line x  10 with foci at
1, 3 and  9, 3
_________________________ 21. Vertical hyperbola with asymptotes y  2 x  3 and y  2 x  5 and the
difference of the focal radii is 8
_________________________ 22. Hyperbola vertices at  5, 7  and  5, 9  and length of the conjugate axis is 8
_________________________ 23. Hyperbola with center  2, 2  , a focus at  2, 2  and and length of the
conjugate axis is 4
Omit all parabolas
_________________________ 24. parabola with directrix y = 3 and a focus at (1, 2)
_________________________ 25. parabola with directrix x  
9
and a vertex at (-2, 3)
4
_________________________ 26. parabola where the directrix is the x-axis and the focus is (5, 1)
_________________________ 27. parabola with the vertex at the center of the hyperbola
9 x 2  4 y 2  90 x  8 y  185  0 and the focus at the center of the circle
x 2  y 2  4 x  2 y  20  0
_________________________ 28. circle whose diameter is the line segment joining the vertex and the focus of the
parabola x 2  12 y  0
Graph each of the following and indicate the domain and range.
29. y  2 1  x 2
30. x  9   y  2 
32. x   25  4y  y 2
33. x   9  9y 2
2
31. x  1  y  3 OMIT
34. y  2  36  4  x  1
2