ANY TANGENT TO AN ELLIPSE IS CUT BY THE TANGENTS AT THE ENDS OF THE MAJOR AND MINOR AXIS IN T AND T^. PROVE TT^ IS DIAMETER PASSES THROUGH FOCI

SHAIK AASIF AHAMED
7 years ago
Hello student,
equation of tangent at$\phi$is$\frac{xcos\phi }{a}+\frac{ysin\phi }{b}=1$….........(1)
tangents at the end of major axis are x=a and x=-a
so T=(a,b tan $\phi$/2) , T1=(-a,bcot$\phi$/2)
The circle on TT1 as diameter is
clearly 2 passes through the foci(ae,0) and (-ae,0)
Thanks and regards
Shaik Aasif