MathDB
Parabolas

Source: All Russian Olympiad 2017,Day1,grade 10,P1

May 3, 2017
algebraconicsparabola

Problem Statement

f1(x)=x2+p1x+q1,f2(x)=x2+p2x+q2f_1(x)=x^2+p_1x+q_1,f_2(x)=x^2+p_2x+q_2 are two parabolas. l1l_1 and l2l_2 are two not parallel lines. It is knows, that segments, that cuted on the l1l_1 by parabolas are equals, and segments, that cuted on the l2l_2 by parabolas are equals too. Prove, that parabolas are equals.
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