OFSA SOLUTIONS for Conics B (Partial)

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
What is the equation for this graph?:

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A:

B:

C:

D:


Solution 1
C:

Error Explanation 1
A is not correct, because the left side of the graph is showing, which means it must be an x= equation, and negative. This also rules out D as an answer.
B is not correct because the shifts are reversed, meaning the number outside the radical is now the horizontal shift, and the number inside the parenthesis with the y is now the vertical shift.
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Question 2
What is the equation for this graph?:
eyr7p5axh3.png
A:

B:

C:

D:


Solution 2
A:

Error Explanation 2
Inside each hyperbola is an imaginary ellipse with a horizontal radius (in which this case shows how far apart the parts of the hyperbola are) and a vertical radius (which is only used to find the slope of the asymptote).
B is not correct because the fraction in front of the radical is the horizontal radius over the vertical radius, as well as the slope of the asymptote. It is flipped in B.
C is not correct, because the number under the radical,

is the horizontal radius of the graph, not the vertical radius.
D is not correct, because the format described graphs a vertical hyperbola, and the graph shown is a horizontal hyperbola.
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Question 3
The Parametric equation:

is equal to which equation?
x=4csc(t), y= 2cot(t), 0
A:

B:

C:

D:

Solution 3
The solution is
C:

When graphed as their components, the two parts of the parametrics form the graphs:
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and:
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When graphed as a full parametric, they form the graph:
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Error Explanation 3
A is wrong because the slope is reversed for the asymptotes of the parabola.
B is wrong because it forms an ellipse rather than a hyperbola.
D is wrong because it forms a vertical hyperbola, rather than a horizontal one.
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Question 4
What type of graph does this equation make:


A: Right half of an ellipse
B: Top half of a hyperbola
C: Bottom half of an ellipse
D: Bottom half of a circle

Solution 4
C: Bottom half of an ellipse

Error Explanation 4
A is incorrect because it's a y= equation
B is incorrect because when x^2 is added to the other side, it forms the equation of an Ellipse and NOT a hyperbola
D is incorrect because there is a fraction before the radical in the equation, which tells us that it's not the equation of a cirlce
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Question 5
What is the number in front of the radical for the equation of this graph?

Screen shot 2012-05-31 at 10.03.30 PM.png
A: 1
B: 1/3
C: 5/4
D: 1/2

Solution 5
B: 1/3
Error Explanation 5
A is incorrect because a 1 in front of the radical would make a circle graph
C and D are incorrect because they are not the correct slope of the graph's asymptotes

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Question 6
Which direction does the graph of this equation open up, and what portion of the graph is used?



A: Opens North-South, and uses right portion
B: Opens East-West, and uses left portion
C: Opens North-South, and uses bottom portion
D: Opens East-West, and uses top portion

Solution 6
D: Opens East-West, and uses top portion
because it would seem like the graph opens North-South, but because of the -25, it actually opens East-West and then the positive fraction before the radical tells us to use the top (positive) part of the graph

Error Explanation 6
A is incorrect because it would only use the right portion if the fraction before the radical was positive, and it was an x= equation
B is incorrect because it would only use the left portion if the fraction before the radical was negative
C is incorrect because it would only open North-South if the -25 was +25, and it would only use the bottom portion if the fraction before the radical was negative

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Question 7
What type of conic created by the following equation?



A.) The top half of a parabola
B.) The bottom half of a parabola
C.) The left half of a parabola
D.) The right half of a parabola

Solution 7
The answer is A.

Error Explanation 7
B.) This answer is incorrect because of the lack of a negative sign outside of the radical, if there was a negative sign, then the bottom values would be included.
C.) This answer is incorrect because the parabola opens left-right, not top-down.
D.) This answer is incorrect because the parabola opens left-right, not top-down.

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Question 8
Which of the following is the equation of an ellipse?

A.)

B.)

C.)

D.)


Solution 8
The correct answer is C.

Error Explanation 8
A.) This answer is incorrect because this is an equation of a hyperbola.
B.) This answer is incorrect because this is an equation of a parabola.
D.) This answer is incorrect because this is an equation of a circle.

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Question 9
How does vertical shifting of a hyperbola get affected in the following equation?



A.) a
B.) b
C.) c
D.) d

Solution 9
The answer is D.

Error Explanation 9
A.) This answer is incorrect because a represents the length of the horizontal axis.
B.) This answer is incorrect because b represents the length of the vertical axis.
C.) This answer is incorrect because c represents the horizontal shift.

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Question 10
What type of graph does this equation make?
y=3sqrt(4+x^2)

A.) Bottom half of ellipse
B.) Right half of ellipse
C.) Top half of Hyperbola
D.) Right half of Hyperbola

Solution 10
C.)
Error Explanation 10
A.) The 3 in the front is not negative, so it cannot be the bottom half (negative y values), and it needs to be minus x^2 for an ellipse.
B.) If x and y switched places and it was a minus y^2
D.) If x and y switched places
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Question 11
What is the slope of the asymptotes in the graph from problem 10, If they exist?
A.) 2/9
B.) 9/2
C.) 9
D.) do not exist
Solution 11
B.)
Error Explanation 11
A.) This is the x value over the y value
C.) the x value of the rectangle goes out by 2, not 1
D.) It is a hyperbola, so it must have asymptotes
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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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