Question

another one :(
a series of chords is drawn to the ellipse \[\large \frac{ x^2 }{ a^2 }+\frac{ y^2 }{ b^2 }=1\]
so that their projections on a straighe line which is inclined at an angle \[\large \alpha \] to the major axis are all of constant length C.
find the locus of their middle point

Answer 1

here ive taken a point (h,k)
so the equation of the chord will be
\[\frac{ x-h }{ \cos \theta }=\frac{ y-k }{ \sin \theta }=r \\whuch ~gives~me \\x=h+rcos \theta \\y=k+rsin \theta\]