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Manipal MET2012MathematicsParabola

The mid-point of the line joining the common points of the line 2 x-3 y+8=0 and y^2=8 x is

Options

  1. A(3,2)
  2. B(5,6)
  3. C(4,-1)
  4. D(2,-3)

Correct answer

B. (5,6)

Step-by-step solution

Let (x₁, y₁ ) be the mid-point of the line joining the common points of the given line and the given parabola. Then, the equation of line is aligned & y y₁-4 (x+x₁ )=y₁^2-8 x₁ & 4 x-y y₁+y₁^2-4 x₁=0 aligned This line and 2 x-3 y+8=0 represents the same line. array ll & 4 2 = -y₁ -3 = y₁^2-4 x₁ 8 & y₁=6, y₁^2-4 x₁=16 & y₁=6, x₁= 36-16 4 & y₁=6, x₁=5 array The required point is (5,6) .

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