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)?​

Answer 1

Equation of circle x² + y² = 5

Explanation:

Given circle whose origin is at center, (g , h) = (0 , 0)

And end points of diameter = (-1 , 2) and (1 , -2)

So, Distance of diameter =
`√((x2 - x1)² + (y2 - y1)²)`

So , Diameter =
`√((1 + 1)² + (-2 - -)²)`

or, Diameter =
`√(20)` =
`2√(5)`

Or, D = 2
`√(5)` unit

Now Radius =
`(Diameter)/(2)` =
}{2}[/tex]

so, Radius ( r) =
`√(5)` unit

SO, equation of circle is

(x -0)² + (y - 0)² = r²

i.e Equation of circle x² + y² = 5 Answer