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Question 17 of 18

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M:N:SPR:1

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SAT

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PSAT/NMSQT

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PSAT 10

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Additional Topics in Math

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x squared plus y squared minus 6 x plus 8 y equals 144

The equation of a circle in the xy-plane is shown above. What is the diameter of the circle?

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Correct Answer: 
No
Correct Answer: 
No
Correct Answer: 
No
Correct Answer: 
No

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26

Completing the square yields the equation open parentheses x minus 3 close parentheses squared plus open parentheses y plus 4 close parentheses squared equals 169 comma the standard form of an equation of the circle. Understanding this form results in the equation r squared equals 169 comma which when solved for r gives the value of the radius as 13. Diameter is twice the value of the radius; therefore, the diameter is 26.

Question Difficulty: 
hard
Objective: 

Students must determine a circle property given the equation of the circle.