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AP EAMCET2012MathematicsEllipse

If the line 2 x+5 y=12 intersects the ellipse 4 x^2+5 y^2=20 in two distinct points A and B , then mid-point of A B is

Options

  1. A(0,1)
  2. B(1,2)
  3. C(1,0)
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

Since, the line 2 x+5 y=12 intersect the ellipse 4 x^2+5 y^2=20 array ll & 4 ( 12-5 y 2 )^2+5 y^2=20 & 144+25 y^2-120 y+5 y^2=20 & 30 y^2-120 y+124=0 & 15 y^2-60 y+62=0 & y= 60 (60)^2-4 15 62 2(15) & = 60 3600-3720 30 = 60 -120 30 array Hence, no real value of y exist. Hence, no intersection is possible.

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