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

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 = $\sqrt{(x2 - x1)² + (y2 - y1)²}$

So , Diameter = $\sqrt{(1 + 1)² + (-2 - -)²}$

or, Diameter = $\sqrt{20}$ = $2\sqrt{5}$

Or, D = 2$\sqrt{5}$  unit

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

so, Radius ( r) = $\sqrt{5}$ unit

SO, equation of circle is

(x -0)² + (y - 0)² = r²

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