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Grade 12Algebra

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

sach

12 Years agoGrade 12

1 Answer

SHAIK AASIF AHAMED

12 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

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