Question #856372ca - SAT Suite Question Bank

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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?

$open parenthesis, x minus 8, close parenthesis, squared, plus, open parenthesis, y plus 6, close parenthesis, squared, equals 25$
$open parenthesis, x plus 8, close parenthesis, squared, plus, open parenthesis, y minus 6, close parenthesis, squared, equals 25$
$open parenthesis, x minus 8, close parenthesis, squared, plus, open parenthesis, y plus 6, close parenthesis, squared, equals 5$
$open parenthesis, x plus 8, close parenthesis, squared, plus, open parenthesis, y minus 6, close parenthesis, squared, equals 5$

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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 $the square root of 5$ .

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