Question

a degenerate circle is:
i. a circle with radius ( r = 0 ).
ii. a point.
iii. a line.
i only
iii only
i and ii only
ii only
i, ii, and iii

Explanation:

A degenerate circle occurs when the radius \(r = 0\). In this case, the set of points that satisfy the circle equation \((x - a)^2+(y - b)^2=r^2\) (where \((a,b)\) is the center) becomes \((x - a)^2+(y - b)^2 = 0\), which implies \(x=a\) and \(y = b\), representing a single point. A line is not related to a degenerate circle as the geometric interpretation of a degenerate circle (with \(r = 0\)) is a point, not a one - dimensional figure like a line.

Answer:

I and II only