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If F1 and F2 are the feet of the per...

If `F_1` and `F_2` are the feet of the perpendiculars from the foci `S_1a n dS_2` of the ellipse `(x^2)/(25)+(y^2)/(16)=1` on the tangent at any point `P` on the ellipse, then prove that `S_1F_1+S_2F_2geq8.`

Text Solution

Verified by Experts

We know that the product of perpendicular from two foci of an ellipse upon any tanegent is equal to the square of the semi-minor axis
Then `(S_(1)F_(1))*(S_(2)F)(2))=16`
Now, `A.M.geG.M.`
`rArr(S_(1)F_(1)+S_(2)F_(2))/(2)gesqrt(S_(1)F_(1)xxS_(2)F_(2))`
`rArr S_(1)F_(1)+S_(2)F_(2)ge8`
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