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Solution


Q.

The equation of the chord, of the ellipse x225+y216=1, whose mid-point is (3, 1) is :          [2025]
1 4x + 122y = 134  
2 5x + 16y = 31  
3 25x + 101y = 176  
4 48x + 25y = 169  

Ans.

(4)

Given: Ellipse is x225+y216=1 and mid-point is (3, 1).

The equation of chord with given middle point is given by

T = S1

⇒ 3x25+1y16–1=925+116–1

⇒ 3x25+y16=925+116

⇒48x+25y=144+25

⇒ 48x+25y=169.