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.
x^2 + y^2 =1 y = 3x + 1 x^2 + (3x + 1)^2 = 1 x^2 + 9x^2 + 6x+ 1 = 1 10x^2 + 6x = 0 x(10x+6) = 0 x= 0 or x = -6/10 = -3/5 When x = 0, y = 1 When x = -3/5, y = -4/5
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