Equation of two lines

Geometry Level 4

y 2 300 x y 100000 x 2 2 y + 1000 x = 0 \large y^2 - 300xy - 100000 x^2 - 2y +1000x = 0

Let A A be the area bounded by the curve above and the x x -axis. Find 10000 A \lfloor 10000A \rfloor .

Notation : \lfloor \cdot \rfloor denotes the floor function .


The answer is 71.

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1 solution

Two lines cut a length of .01 on the x-axis and meet at a height 1.4286.
So the bounded triangular area =1/2 * .01 * 1.4286=0.007143.
10000 * .007143=71.

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