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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)?​

Respuesta :

Answer:

Equation of circle x² + y² = 5

Step-by-step 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 = [tex]\sqrt{(x2 - x1)² + (y2 - y1)²}[/tex]

So , Diameter = [tex]\sqrt{(1 + 1)² + (-2 - -)²}[/tex]

or, Diameter = [tex]\sqrt{20}[/tex] = [tex]2\sqrt{5}[/tex]

Or, D = 2[tex]\sqrt{5}[/tex]  unit

Now Radius = [tex]\frac{Diameter}{2}[/tex] =  [tex]\frac{2[tex]\sqrt{2}[/tex]}{2}[/tex]

so, Radius ( r) = [tex]\sqrt{5}[/tex] unit

SO, equation of circle is

(x -0)² + (y - 0)² = r²

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

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