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The length of the chord of the ellipse x225+ y216=1, whose mid point is (1, 25 ), is equal to :
(1) 16915
Chord with given mid-point: T=S1
x25+ 2y5 16= 125+ 425 16
8x+5y=10, slope m=- 85
Put y= 10-8x5 in the ellipse: 16x2+(10-8x)2=400
4x2-8x-15=0 x1+x2=2, x1x2=- 154
(x1-x2)2=4+15=19
Length =|x1-x2| 1+m2
= 19 895= 16915
Answer: (1)
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