Respuesta :
Answer:
The standard form of the equation of the circle is [tex]x^2+y^2=1[/tex].
Step-by-step explanation:
A circle is the set of points in a plane that lie a fixed distance, called the radius, from any point, called the center.
The equation of a circle in standard form is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where r is the radius of the circle, and h, k are the coordinates of its center.
When the center of the circle coincides with the origin [tex]h=k=0[/tex], so
[tex](x-0)^2+(y-0)^2=r^2\\x^2+y^2=r^2[/tex]
We are also told that the circle contains the point (0, 1), so we will use that information to find the radius r.
[tex]0^2+1^2=r^2\\r^2=0^2+1^2\\r^2=1\\r=\sqrt{1}[/tex]
Therefore, the standard form of the equation of the circle is [tex]x^2+y^2=1[/tex].
