Which of the following is the equation of a circle whose center is at the origin and whose diameter has endpoints (-1,2) and (1,-2)? a.) x^2 + y^2 = 2 b.) x^2 + y^2 = 3 c.) x^2 + y^2 = 4 d.) x^2 + y^2 = 5

D

The equation of a circle centred at the origin is x² + y² = r²

where r is the radius. the radius is the distance from the centre to either of the endpoints of the diameter

use the distance formula to calculate r with endpoint (1, - 2)

r = √(1² + (- 2)² = √(1 + 4) = √5 ⇒ r² = (√5)² = 5

equation is x² + y² = 5

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step-by-step explanation: