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A continuous signal is a signal which is continuous w.r.t time for example Sinwt where t=R(real numbers).
that means you can have some value of signal at any instant of time like 0.0000009 secs or 11.999999993 secs.
A DC signal is definitely a continuous signal, but whether it is an analog signal or not that is difficult to say.
To know clearly the topic of signals once you need to understand Pulse Code Modulation.
How an analog signal is converted to Digital signal using first sampling then quantisation and then encoding.
An analog signal can have any value as opposed to a digital signal that could only have two values. A discrete analog signal can only have predefined values. For example the output of a DAC (Digital to analog converter). A continuous signal is an analog signal that can take any value and the distance between any two contiguous values is infinitesimal. Generally this is the kind of signals that you get in linear (or analog circuits)
A DC signal could result from a linear circuit, as at the output of a voltage regulator, Or at the output of a digital gate or at the output of a DAC. An also can be the input to a digital or analog system. So it depends on the application.