We will have the following:
*First: We have that the equation of the circle will be given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Here (h, k) is the coordinate of the center of the circle and r is the radius of the circle.
*Second: We will replace the center of the circle and determine the radius:
[tex]x^2+y^2=r^2[/tex]*Third: We determine the radius of the circle by using the point given:
[tex](0)^2+(3)^2=r^2\Rightarrow r^2=9\Rightarrow r=3[/tex]*Fourth: We have the following expression representing the circle:
[tex]x^2+y^2=9[/tex]So, we replace the point (-2, sqrt(5)) to determine whether or not it belongs to the circle, that is:
[tex](-2)^2+(\sqrt[]{5})^2=9\Rightarrow4+5=9\Rightarrow9=9[/tex]Thus proving that the point (-2, sqrt(5)) does lie in the circle.
