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If the ellipse 9 x^2+16 y^2=144 intercepts the line 3 x+4 y=12 , then what is the length of the chord so formed?

Options

  1. A5 units
  2. B6 units
  3. C8 units
  4. D10 units

Correct answer

A. 5 units

Step-by-step solution

Here, 9 x^2+16 y^2=144 and 3 x+4 y=12 x= 12-4 y 3 So, 9 ( 12-4 y 3 )^2+16 y^2=144 On solving we get, y=0,3 For y=0 ; x=4 For y=3 ; x=0 aligned Length of chord = & (0-3)^2+(4-0)^2 = 9+16 & = 25 =5 units aligned

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