Paper 2 October/November 2001 MATHEMATICH (8709/2) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

A curve has equation $y = k{x^2} + 1$ and a line has equation $y = kx$, where $k$ is a non-zero constant.
a) Find the set of values of $k$ for which the curve and the line have no common points.
b) State the value of $k$ for which the line is a tangent to the curve and, for this case, find the coordinates of the point where the line touches the curve.