MathDB

15

Part of 2005 National High School Mathematics League

Problems(1)

Analytic Geometry

Source: 2005 National High School Mathematics League, Exam One, Problem 15

3/20/2020
A(1,1)A(1,1) is a point on parabola y=x2y=x^2. Draw the tangent line of the parabola that passes AA, the line intersects xx-axis at DD, intersects yy-axis at BB. CC is a point on the parabola, and EE is a point on segment ACAC, such that AEEC=λ1\frac{AE}{EC}=\lambda_1, FF is a point on segment BCBC, such that BFFC=λ2\frac{BF}{FC}=\lambda_2. If λ1+λ2=1\lambda_1+\lambda_2=1, CDCD and EFEF intersect at PP. When CC moves, find the path equation of PP.
conicsparabolaanalytic geometrygeometry