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 equation for a line is y(x)=ax+b.Because it intersects the y axis at x=0 at y=1y(x)=b=1a is equal to the gradient of the function so the line is given as y(x)=3x+1In order to get the two intersections we need to solve the following equation system:(1) x²+y²=1(2) y=3x+1
(1) x²+(3x+1)²=1 x²+9x² +1+6x=1 10x²+6x=0Then solving it for x we get x=0 y=1 and x=-3/5 y=-4/5