Question

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

Answer 1

the answer is D.) x^2 + y^2 = 5

Answer 2

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