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JEE Advanced2021MathematicsStraight LinesActual

Consider a triangle Δ whose two sides lie on the x -axis and the line x + y + 1 = 0 . If the orthocenter of Δ is ( 1 , 1 ) , then the equation of the circle passing through the vertices of the triangle Δ is

Options

  1. Ax 2 + y 2 - 3 x + y = 0
  2. Bx 2 + y 2 + x + 3 y = 0
  3. Cx 2 + y 2 + 2 y - 1 = 0
  4. Dx 2 + y 2 + x + y = 0

Correct answer

B. x 2 + y 2 + x + 3 y = 0

Step-by-step solution

Let A is the point of intersection of the given lines y = 0 ,   x + y + 1 = 0 Their point of intersection A is - 1 , 0 Let B is the other point on the line x + y + 1 = 0 , Now, the perpendicular from B on the x -axis will pass through the orthocenter. So, the equation of perpendicular from B on the x -axis is x = 1 Thus, the coordinates of B are 1 , - 2 Let the third vertex is h , k Slope of the line perpendicular to x + y + 1 = 0 is 1 So, the perpendicular from h , k to line x + y + 1 = 0 has slope 1 and pass

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