How many tangent lines pass through...

Hi

Posting this because I don't know how to go about doing it (I'm sure the actual math is easy, just the process). Anyways, it asks how many tangent lines pass through the curve y = x^2 + 2x through the point (-1/2,-3). The differentiated equation is y'=2x + 2 but how exactly would you find the number of curves passing through that?

My second question's on Lemniscate's curve (the figure 8). The equation is y^2 = x^2 - x^4. I don't understand what it means when asking "find dy/dx or y' at (1/2, sqrt3/4). Would I just plug in these two coordinates for y and x after implicitly differentiating? I get y' = 1-2x^2/1-x^2 after implicitly differentiating this.