Question

find the standard form of the equation of the circle having the following properties: center at the origin containing the point (-1,1) type the standard form of the equation of this circle.

Explanation:

Step1: Recall circle - equation formula

The standard - form equation of a circle with center \((h,k)\) and radius \(r\) is \((x - h)^2+(y - k)^2=r^2\). Since the center is at the origin \((0,0)\), the equation becomes \(x^{2}+y^{2}=r^{2}\).

Step2: Calculate the radius

The circle contains the point \((-1,1)\). Substitute \(x=-1\) and \(y = 1\) into the equation \(x^{2}+y^{2}=r^{2}\). We get \((-1)^{2}+1^{2}=r^{2}\), which simplifies to \(1 + 1=r^{2}\), so \(r^{2}=2\).

Answer:

\(x^{2}+y^{2}=2\)