Re: Algebra with discriminant of the quadratic polynomial.

On Thu, 21 Aug 2008, Virgil wrote:

On Mon, 18 Aug 2008, mina_world wrote:

x^2 + y^2 = 4.
y = x^2 + k.

Find all point which have common tangent line
between x^2 + y^2 = 4 and y = x^2 + k.

For k = 2 and k = -2, there will be exactly one point of tangency at the
vertex of the parabola, i.e,. at (0,k).

For k = -17/4, there will be two points of tangency
at (+/- sqrt(15)/2, -1/2).

For other values of k, there will not be any points of tangency.

Does the problem read
find lines tangent to both curves
or
find lines tangent to both curves at their points of intersection?

.

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