When Lady Capulet says to Juliet, "Speak briefly, can you like of Paris' love?", what does this suggest to an audience about their relationship?
The line itself comes just after a pretty long speech of Lady Capulet's (lines 79-94 in Act I, scene iv) about how handsome Paris is, how rich, and what a catch that makes him for Juliet. The line you have quoted is notable for two of Lady Capulet's phrasing choices.
First, her admonishment to "Speak briefly," could mean that she takes a very classically parental stance with Juliet -- children are to be seen and not heard, so Juliet should not presume to go on and on in her conversation. It could also mean that she isn't very interested in what Juliet has to say, so Juliet should cut to the chase, as it were. It could also hint that Juliet is a very smart cookie, smarter than her mother perhaps, and that Lady Capulet doesn't want one of Juliet's long, drawn-out speeches.
The second thing to note about Lady Capulet's question, "can you like of Paris' love?" is that she expects an answer from Juliet simply based solely upon her (Lady Capulet's) description of him. This suggests that Lady Capulet is not that interested in Juliet's point of view (since Juliet would have to actually meet Paris to form her own opinion), or simply assumes that it will be the same as her own. The action of the rest of the play would bear out the observation that, if Lady Capulet assumes her daughter's opinion will be similar to her own, she does not know her daughter very well, and, hence, must not have a very close relationship with her.
In fact, Juliet's line that follows:
I'll look to like, if looking liking move,
But no more deep will I endart mine eye
Than you consent gives strenght to make it fly.
suggests both that Juliet is capable of a very wise and witty turn of words and that she doesn't hold much faith in her mother's point of view or "consent."
These facts, plus the balance of the events of the play, suggest to me that Juliet and her mother have a distant, formal relationship.
This line (from I, iii) suggests to the audience that they really have a very good relationship and that Lady Capulet is extraordinarily respectful of her daughter's wishes. You can tell that by thinking about what is going on in this scene.
Paris has asked Juliet's parents if he can marry her. This is back in the days when parents made these kinds of decisions for their kids. But Juliet's mother is asking her her opinion. She is asking her if she could possibly love Paris. This implies that Lady Capulet cares about what Juliet thinks and will let Juliet's opinion have some impact on her (and Lord Capulet's) decision about Paris's request.
So we can see from this that Lady Capulet and her daughter have a very good relationship.