Question

which of the following is the correct equation for the unit circle? (1 point)
○ (x)^2+(y)^2 = 1
○ (x)^2-(y)^2 = 4
○ (x)^2+(y)^2 = 4
○ (x)^2-(y)^2 = 9

Explanation:

Step1: Recall circle - equation formula

The general equation of a circle with center \((h,k)\) and radius \(r\) is \((x - h)^2+(y - k)^2=r^2\). For a unit - circle, the center is at the origin \((0,0)\) and the radius \(r = 1\).

Step2: Substitute values into the formula

Substituting \(h = 0\), \(k = 0\), and \(r = 1\) into the general circle equation \((x - h)^2+(y - k)^2=r^2\), we get \((x-0)^2+(y - 0)^2=1^2\), which simplifies to \(x^{2}+y^{2}=1\).

Answer:

\((x)^{2}+(y)^{2}=1\)