The locus of the midpoints of all chords of the parabola defined by the equation y2=4ax that pass through the vertex is proven to be the parabola described by y2=2ax. The midpoint of a chord connecting the vertex and a point (h, 2√(ah)) on the parabola is calculated as (h/2, √(ah)). By eliminating the variable h, the relationship between x and y is established, confirming the locus as y2=2ax.
PREREQUISITESStudents studying coordinate geometry, mathematics educators, and anyone interested in the properties of parabolas and their applications in geometric proofs.
Pranav-Arora said:Homework Statement
Prove that the locus of middle points of all chords of the parabola ##y^2=4ax## which are drawn through the vertex is the parabola ##y^2=2ax##.
Homework Equations
The Attempt at a Solution
The mid-point of the line joining the vertex and a point ##(h,2\sqrt{ah})## on parabola is ##(h/2,\sqrt{ah})## but what am I supposed to do with this?
I like Serena said:
