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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

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

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
equation of tangent at\phiis\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
240-1374_12.PNG
clearly 2 passes through the foci(ae,0) and (-ae,0)
Thanks and regards
Shaik Aasif
askIITians faculty

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