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Test
Math
Domain
Geometry and Trigonometry
Skill
Circles
Difficulty
Medium
ID: 856372ca
Modded SAT Question Bank by Abdullah Mallik

In the xy-plane, a circle with radius 5 has center with coordinates negative 8 comma 6. Which of the following is an equation of the circle?

  1. open parenthesis, x minus 8, close parenthesis, squared, plus, open parenthesis, y plus 6, close parenthesis, squared, equals 25

  2. open parenthesis, x plus 8, close parenthesis, squared, plus, open parenthesis, y minus 6, close parenthesis, squared, equals 25

  3. open parenthesis, x minus 8, close parenthesis, squared, plus, open parenthesis, y plus 6, close parenthesis, squared, equals 5

  4. open parenthesis, x plus 8, close parenthesis, squared, plus, open parenthesis, y minus 6, close parenthesis, squared, equals 5

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Correct Answer: B
Rationale

Choice B is correct. An equation of a circle is open parenthesis, x minus h, close parenthesis, squared, plus, open parenthesis, y minus k, close parenthesis, squared, equals r squared, where the center of the circle is the point with coordinates h comma k and the radius is r. It’s given that the center of this circle is the point with coordinates negative 8 comma 6 and the radius is 5. Substituting these values into the equation gives open parenthesis, x minus negative 8, close parenthesis, squared, plus, open parenthesis, y minus 6, close parenthesis, squared, equals 5 squared, or open parenthesis, x plus 8, close parenthesis, squared, plus, open parenthesis, y minus 6, close parenthesis, squared, equals 25.

Choice A is incorrect. This is an equation of a circle that has center 8 comma negative 6. Choice C is incorrect. This is an equation of a circle that has center 8 comma negative 6 and radius the square root of 5. Choice D is incorrect. This is an equation of a circle that has radius  the square root of 5.

Question Difficulty: Medium
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