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Finding a Tangent Line to a Parabola

​
m
-1
There is a neat method for finding tangent lines to a parabola that does not involve calculus. In this problem, for example, to find the line tangent to
y=
2
x
-3
at (1, -2) we can simultaneously solve
y=
2
x
-3
and
y+2=m(x-1)
and set the discriminant equal to zero, which means that we want only one solution to the system (i.e., we want only one point of intersection).

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