Question

Write the standard form of the equation of the circle that passes through the point

Answer 1

Answer:

The standard form of the equation of the circle is $x^2+y^2=1$.

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

                                             $(x-h)^2+(y-k)^2=r^2$

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 $h=k=0$, so

                                            $(x-0)^2+(y-0)^2=r^2\\x^2+y^2=r^2$

We are also told that the circle contains the point  (0, 1), so we will use that information to find the radius r.

                                                   $0^2+1^2=r^2\\r^2=0^2+1^2\\r^2=1\\r=\sqrt{1}$

Therefore, the standard form of the equation of the circle is $x^2+y^2=1$.