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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

The number of distinct possible lines passing through the point 2 , 3 and forming a triangle with the coordinate axes whose area is 12 s q . units, is/are

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

C. 3

Step-by-step solution

Equation of any line through 2,3 is y - 3 = m x - 2 y = m x - 2 m + 3 From the figure, Area of ∆ O A B = 12 sq. units i.e., 1 2 2 m - 3 m 3 - 2 m = ± 12 taking positive sign, we get 2 m + 3 2 = 0 this gives one value of m = - 3 2 and by taking negative sign, we get 4 m 2 - 36 m + 9 = 0 which is a quadratic in m whose discriminant is greater than 0 , so it gives 2 values of m ⇒ 3 lines are possible.

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