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.

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.
Click here to return to OFSA. 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.
Click here to return to OFSA. 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.
Click here to return to OFSA. 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
Click here to return to OFSA. 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
Click here to return to OFSA. 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
Click here to return to OFSA. 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.

Click here to return to OFSA. Question 8 Solution 8 Error Explanation 8
Click here to return to OFSA. Question 9 Solution 9 Error Explanation 9
Click here to return to OFSA. Question 10 Solution 10 Error Explanation 10
Click here to return to OFSA. Question 11 Solution 11 Error Explanation 11
Click here to return to OFSA. Question 12 Solution 12 Error Explanation 12
Click here to return to OFSA. Question 13 Solution 13 Error Explanation 13
Click here to return to OFSA. Question 14 Solution 14 Error Explanation 14
Click here to return to OFSA. Question 15 Solution 15 Error Explanation 15
Click here to return to OFSA. Question 16 Solution 16 Error Explanation 16
Click here to return to OFSA. Question 17 Solution 17 Error Explanation 17
Click here to return to OFSA. Question 18 Solution 18 Error Explanation 18
Click here to return to OFSA. Question 19 Solution 19 Error Explanation 19
Click here to return to OFSA. Question 20 Solution 20 Error Explanation 20
Click here to return to OFSA. Question 21 Solution 21 Error Explanation 21
Click here to return to OFSA. Question 22 Solution 22 Error Explanation 22
Click here to return to OFSA. Question 23 Solution 23 Error Explanation 23
Click here to return to OFSA. Question 24 Solution 24 Error Explanation 24
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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 DirectionsQuestion 1Solution 1b. 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 1a. 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.

Click here to return to OFSA.

Question 2Solution 2c. 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 2a. 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.

Click here to return to OFSA.

Question 3Solution 3a. 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 3b. 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.

Click here to return to OFSA.

Question 4Solution 4a. is correct because if you complete the square you get the equation of the conic

Error Explanation 4b. 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

Click here to return to OFSA.

Question 5Solution 5b. is correct because the value under x should be 25 and the value under y should be 4.

Error Explanation 5a. 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

Click here to return to OFSA.

Question 6Solution 6d. is correct because an ellipse is x+y and the values below the x and y should be 16 and 9 respectively

Error Explanation 6a. 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

Click here to return to OFSA.

Question 7Which way does the equation x=-4sqrt(9+y^2) open?Solution 7It opens right.

Error Explanation 7The equation is an x hyperbola, and since the negative is outside the square root, only the left side of the graph is drawn.

Click here to return to OFSA.

Question 8Solution 8Error Explanation 8Click here to return to OFSA.

Question 9Solution 9Error Explanation 9Click here to return to OFSA.

Question 10Solution 10Error Explanation 10Click here to return to OFSA.

Question 11Solution 11Error Explanation 11Click here to return to OFSA.

Question 12Solution 12Error Explanation 12Click here to return to OFSA.

Question 13Solution 13Error Explanation 13Click here to return to OFSA.

Question 14Solution 14Error Explanation 14Click here to return to OFSA.

Question 15Solution 15Error Explanation 15Click here to return to OFSA.

Question 16Solution 16Error Explanation 16Click here to return to OFSA.

Question 17Solution 17Error Explanation 17Click here to return to OFSA.

Question 18Solution 18Error Explanation 18Click here to return to OFSA.

Question 19Solution 19Error Explanation 19Click here to return to OFSA.

Question 20Solution 20Error Explanation 20Click here to return to OFSA.

Question 21Solution 21Error Explanation 21Click here to return to OFSA.

Question 22Solution 22Error Explanation 22Click here to return to OFSA.

Question 23Solution 23Error Explanation 23Click here to return to OFSA.

Question 24Solution 24Error Explanation 24Click here to return to OFSA.