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Maths-

SAT

Easy

Question

In the xy-plane, the points (-3, 10) and (3, 10) are endpoints of the diameter of a circle. Which equation represents this circle?

x²+ (y -10)² = 9
(x+3)²+y² =36
(x + 3)² + (y -10)² = 9
(x + 3)² + (y -10)² = 36

The correct answer is: x²+ (y -10)² = 9

(-3, 10) (3, 10)
Distance = $square root of open parentheses x subscript 2 minus x subscript 1 close parentheses squared plus open parentheses y subscript 2 minus y subscript 1 close parentheses squared end root$
$square root of left parenthesis 0 minus left parenthesis negative 3 right parenthesis right parenthesis squared plus left parenthesis 10 minus 10 right parenthesis squared end root$
r = $square root of left parenthesis 3 right parenthesis squared end root equals 3$
Mid point = $open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction comma fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction close parentheses equals open parentheses fraction numerator negative 3 plus 3 over denominator 2 end fraction comma fraction numerator 10 plus 10 over denominator 2 end fraction close parentheses equals left parenthesis 0 comma 10 right parenthesis$
Equation of the circle = (x - h)² + (y - k)² = r²
(x - 0)² + (y - 10)² = 3²
x² + (y - 10)² = 9

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