completely stuck here:

1. find the value of k for which y = 3x+1 is a tangent to the curve

x^2 + y^2 = k

2. find the range of values of k for which y=x-3 meets x^2-3y^2=k in two distinct points.

and i went wrong in this question, no idea where though

find the number of points of intersection

y= x/4 + 1

y^2 = x

i multiplied by 4 to get rid of the fraction. do i square root x ??