OFSA SOLUTIONS for Conics A (Full)

This page contains peer generated solutions and error explanations to OFSA questions. As you read or view the solutions, be critical: check for accuracy, but also for more efficient solution strategies. If you have a better method or different idea/answer, post a discussion and monitor the responses.

Quick Directions
  • Post answers, solutions and error explanations to each OFSA question below.
  • For each "distractor" or incorrect answer choice, explain the error that would lead to that incorrect answer choice.
  • You may either do the above in typed format or using a pencast.
  • Separate each question with a section bar.
  • After each solution, provide a hyperlink back to the corresponding OFSA page.
  • Follow example below.
  • Click here to refer to solution format in 7.7



Question 1
Solution 1
b. is correct because the a term is with the x and the b term is with the y. Also there is a negative and the equation is equal to 1.
Error Explanation 1
a. is wrong because the a and b terms are switched.
c. is wrong because it has a plus instead of a minus. It is the general equation of an ellipse.
d. is wrong because it has no a or b term at all. It would be the equation of a circle if the minus was a plus.
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Question 2
Solution 2
c. is correct because the plus indicates an ellipse and it has the correct center at (0,4). The c value can be found from distance between the foci divided by 2 and then using the eccentricity to find a as 6. Then using the relationship

we find b as

Error Explanation 2
a. is wrong because the a and b terms are not squared.
b. is wrong because the center of the ellipse is incorrectly identified as (3,-4).
d. is wrong because it is the equation of a hyperbola.
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Question 3
Solution 3
a. is correct because it is 2 left of the vertex. The value of p can be found from the focal diameter = 4p. The focus is on the axis of symmetry a distance p away from the vertex in the dircetion that the parabola opens.
Error Explanation 3
b. is wrong because it is in the opposite direction.
c. is wrong because it is too far. The point is 2p away from the vertex.
d. is wrong because it is a distance p up, not to the left.
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Question 4
Solution 4
a. is correct because if you complete the square you get the equation of the conic
Error Explanation 4
b. is wrong because the end term must be 81 since 68+4+9 = 81
c. is wrong because the square was completed incorrectly and the radius is said to be 1
d. is wrong because the square was completed incorrectly
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Question 5
Solution 5
b. is correct because the value under x should be 25 and the value under y should be 4.
Error Explanation 5
a. is wrong because the hyperbola opens north/south when it should open east/west
c. is wrong because the 4 should be under y and the 25 should be under x also that hyperbola opens n/s instead of e/w
d. is wrong because the 4 should be under y and the 25 should be under x
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Question 6
Solution 6
d. is correct because an ellipse is x+y and the values below the x and y should be 16 and 9 respectively
Error Explanation 6
a. is wrong because the a and b values aren't squared
b. is wrong because it is x-y and that is for hyperbolas also the a and b values need to be squared.
c. is wrong because x-y is for hyperbolas
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Question 7
Which way does the equation x=-4sqrt(9+y^2) open?
Solution 7
It opens right.
Error Explanation 7
The equation is an x hyperbola, and since the negative is outside the square root, only the left side of the graph is drawn.

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Question 8
Solution 8
Error Explanation 8
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Question 9
Solution 9
Error Explanation 9
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Question 10
Solution 10
Error Explanation 10
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Question 11
Solution 11
Error Explanation 11
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Question 12
Solution 12
Error Explanation 12
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Question 13
Solution 13
Error Explanation 13
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Question 14
Solution 14
Error Explanation 14
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Question 15
Solution 15
Error Explanation 15
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Question 16
Solution 16
Error Explanation 16
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Question 17
Solution 17
Error Explanation 17
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Question 18
Solution 18
Error Explanation 18
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Question 19
Solution 19
Error Explanation 19
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Question 20
Solution 20
Error Explanation 20
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Question 21
Solution 21
Error Explanation 21
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Question 22
Solution 22
Error Explanation 22
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Question 23
Solution 23
Error Explanation 23
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Question 24
Solution 24
Error Explanation 24
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