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BITSAT2024MathematicsParabolaActual

Let L₁ be the length of the common chord of the curves x^2+y^2=9 and y^2=8 x , and L₂ be the length of the latus rectum of y^2=8 x , then:

Options

  1. AL ₁ L ₂
  2. BL ₁= L ₂
  3. CL ₁ L ₂
  4. DL ₁ ~L ₂ = 2

Correct answer

C. L ₁ L ₂

Step-by-step solution

We have : x^2+(8 x)=9 x^2+9 x-x-9=0 x(x+9)-1(x+9)=0 (x+9)(x-1)=0 x=-9,1 for x=1, y= 2 2 x = 2 2 (2 2 +2 2 )^2+(1-1)^2 =4 2 L _n= Length of latus rectum =4 a=4 2=8 L ₁ L ₂

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