



 
Carter, Suppose that a tangent to the curve y = x^{2} + 1 at the point P on the curve with coordinates (a, b) passes through (2, 0). Since (a, b) lies on the curve b = a^{2} + 1. The slope of the tangent at P is the derivative of y = x^{2} + 1 at x = a which is 2a. Thus the equation of the tangent line is
But (2, 0) is on the tangent so
Substitute b = a^{2} + 1 to get
Solve for a. Penny  


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