ON TRIANGLES ASSOCIATED WITH A CURVE
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It is well-known that the area of parabolic region between a parabola and any chord P1P2 on the parabola is four thirds of the area of triangle △P1P2P. Here we denote by P the point on the parabola where the tangent is parallel to the chord P1P2. In the previous works, the first and third authors of the present paper proved that this property is a characteristic one of parabolas. In this paper, with respect to triangles △P1P2Q where Q is the intersection point of two tangents to X at P1 and P2 we establish some characterization theorems for parabolas.
Abstract
It is well-known that the area of parabolic region between a parabola and any chord P1P2 on the parabola is four thirds of the area of triangle △P1P2P. Here we denote by P the point on the parabola where the tangent is parallel to the chord P1P2. In the previous works, the first and third authors of the present paper proved that this property is a characteristic one of parabolas. In this paper, with respect to triangles △P1P2Q where Q is the intersection point of two tangents to X at P1 and P2 we establish some characterization theorems for parabolas.
참고문헌 (16)
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