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Maths-

SAT

Easy

Question

In the xy-plane, the points (2, 4) and (-2, -4) are the endpoints of a diameter of a circle, Which of the following is an equation of the circle?

(x-2)² +(y+4)² = 80
(x-2)² + (y+4)² = 20
x² + y ² = 80
x² + y² = 20

The correct answer is: x² + y² = 20

Centre = midpoint of (2,4) & (-2, -4)
$equals open parentheses fraction numerator 2 minus 2 over denominator 2 end fraction comma fraction numerator 4 minus 4 over denominator 2 end fraction close parentheses equals left parenthesis 0 comma 0 right parenthesis$
Diameter = $square root of left parenthesis 2 plus 2 right parenthesis squared plus left parenthesis 4 plus 4 right parenthesis squared end root equals square root of 4 squared plus 8 squared end root equals square root of 16 plus 64 end root equals square root of 80$
Radius = $fraction numerator square root of 80 over denominator 2 end fraction equals fraction numerator 2 square root of 20 over denominator 2 end fraction equals square root of 20$
Circle equation = x² + y² = 20.

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