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point not on the curve

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A tangent to a curve through a point not on the curve 2008-07-23
Carter pose la question :
How does one find the tangent points on a curve, given only the curve's function and the x-intercept of that tangent line?
i.e. Find the point(s) on the curve y = -(x^2) + 1, where the tangent line passes through the point (2, 0). I know that there will be two such points, one where y is very close to 1, and the other point where y is a large negative number. However, I do not recall how to figure out the tangent line equation given a single intercept and solving to find the tangent points.

Penny Nom lui répond.
 
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