As shown above, are rigid rods and , is fixed on the coordinate plane, and is restricted along the x-axis. Then as moves horizontally, point will rotate around point . Curve is the locus of point .
If line intersects with at point , at point , and is tangent to curve .
Then find the minimum area of when line moves and rotates.
Let be the minimum area. Submit .
Have a look at my problem set: SAT 1000 problems
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Locus of M , assuming the two rods are hinged at their junction and the rod O N is hinged at O , is x 2 + 4 y 2 = 1 6
The triangle △ O P Q will have minimum area when P Q is perpendicular to the x -axis, the minimum area being
2 1 × 4 × 4 = 8 square units, so that the answer is 8 0 0 0