2

Part of 1994 Putnam

Problems(2)

Source:

A

be the area of the region in the first quadrant bounded by the line

y = \frac{x}{2}

, the x-axis, and the ellipse

\frac{x^2}{9} + y^2 = 1

. Find the positive number

m

A

is equal to the area of the region in the first quadrant bounded by the line

y = mx,

the y-axis, and the ellipse

\frac{x^2}{9} + y^2 = 1.

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Source:

For which real numbers

c

is there a straight line that intersects the curve

y = x^4 + 9x^3 + cx^2 + 9x + 4

in four distinct points?

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