11.8+OFSA+Solutions

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?:**

A: math y=-\sqrt{16-x^2}+3 math B: math x=-\sqrt{16-(y-3)^2} math C: math x=-\sqrt{16-y^2}+3 math D: math x=\sqrt{16-y^2}+3 math

C: math x=-\sqrt{16-y^2}+3 math 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. Click here to return to OFSA.
 * __Solution 1__**
 * __Error Explanation 1__**

A: math y=\frac{2}{3}\sqrt{(x+2)^2-4} math B: math y=\frac{3}{2}\sqrt{(x+2)^2-4} math C: math y=\frac{3}{2}\sqrt{(x+2)^2-9} math D: math y=\frac{3}{2}\sqrt{4+(x+2)^2} math
 * Question 2**
 * What is the equation for this graph?:**

A: math y=\frac{2}{3}\sqrt{(x+2)^2-4} math 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, math r^2 math 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. Click here to return to OFSA.
 * __Solution 2__**
 * __Error Explanation 2__**

math x=4csc(t), y= 2cot(t), 0 math x=4csc(t), y= 2cot(t), 0 A: math \frac{x^2}{4}-\frac{y^2}{16}=1 math B: math \frac{x^2}{16}+\frac{y^2}{4}=1 math C: math \frac{x^2}{16}-\frac{y^2}{4}=1 math D: math \frac{y^2}{4}-\frac{x^2}{16}=1 math The solution is C: math \frac{x^2}{16}-\frac{y^2}{4}=1 math When graphed as their components, the two parts of the parametrics form the graphs: and: When graphed as a full parametric, they form the graph: 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. Click here to return to OFSA.
 * Question 3**
 * The Parametric equation:**
 * is equal to which equation?**
 * __Solution 3__**
 * __Error Explanation 3__**

math \[y=-\frac{3}{5}\sqrt{25-x^{2}}\] math
 * 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

C: Bottom half of an ellipse
 * __Solution 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 Click here to return to OFSA.
 * __Error Explanation 4__**


 * Question 5**
 * What is the number in front of the radical for the equation of this graph?**

A: 1 B: 1/3 C: 5/4 D: 1/2

B: 1/3 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
 * __Solution 5__**
 * __Error Explanation 5__**

Click here to return to OFSA.


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

math \[y=\frac{2}{5}\sqrt{(x-3)^{2}-25}\] math

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

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
 * __Solution 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
 * __Error Explanation 6__**

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

math \[x=2\sqrt{25+y}+4\] math

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

The answer is A.
 * __Solution 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.
 * __Error Explanation 7__**

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

A.) math \[\frac{x^{2}}{4}-\frac{y^{2}}{9}=1\] math B.) math \[x=y^{2}-4\] math C.) math \[\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\] math D.) math \[\frac{y^{2}}{9}+\frac{x^{2}}{9}=1\] math

The correct answer is C.
 * __Solution 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.
 * __Error Explanation 8__**

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

math \[\frac{(x-c)^{2}}{a^{2}}-\frac{(y-d)^{2}}{b^{2}}=1\] math

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

The answer is D.
 * __Solution 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.
 * __Error Explanation 9__**

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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

C.) 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 Click here to return to OFSA.
 * __Solution 10__**
 * __Error Explanation 10__**

A.) 2/9 B.) 9/2 C.) 9 D.) do not exist B.) 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 Click here to return to OFSA.
 * Question 11**
 * What is the slope of the asymptotes in the graph from problem 10, If they exist?**
 * __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__**