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Baltic Way
1999 Baltic Way
5
5
Part of
1999 Baltic Way
Problems
(1)
A bit of algebra... Tangent to circle meets parabola
Source: Baltic Way 1999
12/23/2010
The point
(
a
,
b
)
(a,b)
(
a
,
b
)
lies on the circle
x
2
+
y
2
=
1
x^2+y^2=1
x
2
+
y
2
=
1
. The tangent to the circle at this point meets the parabola
y
=
x
2
+
1
y=x^2+1
y
=
x
2
+
1
at exactly one point. Find all such points
(
a
,
b
)
(a,b)
(
a
,
b
)
.
conics
parabola
analytic geometry
slope
quadratics
algebra