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If CF is the perpendicular from the centre C f ellipse x2/a2+ y2/b2 = 1 on the tangent at any point P & G is the point when the normal at P meets the major axis , then CF PG equals to

(a) a2 (b) ab

(c) b2 (d) b3

plzz explain..!!

Ranjita yadav , 13 Years ago
Grade 11
anser 1 Answers
M Murali Krishna

Last Activity: 10 Years ago

Equation of tangent at
P(a costhita, b sinthita) on ellipse is
(x costhita/a) + ( y sinthita/b) = 1.
i.e. bx costhita + ay sinthita = ab.
CF= ab/sqrt (b^2 cos^2thita + a^2 sin^2thita).
Equation of Normal at 
P(a costhita, b sinthita) on ellipse is
ax/ costhita – by/ sinthita =a^2-b^2.
solving with y=0 we get G= ( (a^2-b^2) costhita /a, 0).
By distance formula, PG = (b/a)sqrt (b^2 cos^2thita + a^2 sin^2thita).
CF  PG = b^ 2
 
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