Hi

Find the values of k for which the line  is a tangent to the curve .

 OR y = -.25x^2 +5 Parabola V(0,5)

 y = -kx + 8   Line would be tangent to the Parabola at Pt(3,3)

 3 = -k*3 + 8   k = 5/3



 

Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
 We could use calculus or a graph (actually, the graph still helps as it gives a good visual), but the easiest way to do it is to treat them as functions of y and set them equal.









Since the quadratic is differentiable everywhere, we can say that a tangency point occurs when the equation has only one solution for x. We turn this into a quadratic in terms of x





, set the discriminant equal to zero.











 

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