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NTA Abhyas JEE Main2020MathematicsCirclePractice

A straight line l 1 with equation x - 2 y + 10 = 0 meets the circle with equation x 2 + y 2 = 100 at B in the first quadrant. A line through B , perpendicular to l 1 cuts the x -axis and y -axis at P and Q respectively. The area (in sq. units) of the triangle O P Q is (where, O is the origin)

Options

  1. A120
  2. B150
  3. C100
  4. D125

Correct answer

C. 100

Step-by-step solution

Slope of l 1 = 1 2 Slope of l 2 = - 2 Equation of l 2 is y = - 2 x - 10 ⇒ y + 2 x = 20 Hence, P and Q are 10 , 0 and 0 , 20 Area of ∆ O P Q = 1 2 × 10 × 20 = 100 sq. units

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