The circle c has equation x^2 + y^2 = 1. The line l has gradient 3 and intercepts the y axis at the point (0, 1). c and l intersect at two points. Find the co-ordinates of these points.

The first step would be to form an equation for the line l. Using y=mx+c, and the information provided in the question, the equation for line l is y=3x+1. To find the coordinates of where c and l intersect, substitute y=3x+1 into the equation of the circle. Expanding the brackets gives 10x^2 +6x=0. Rewritten as x(10x+6), the values of x can be worked out as 0 and -3/5. Substituting these values back into the equation of line l gives you the respective y values. The coordinates for these two points are (0,1) and (-3/5, -4/5)