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MHT CET202620 April 2026Morning ShiftMathematicsStraight LinesActual

The area of a triangle formed by a line with the coordinate axes is 49 sq. units. If the perpendicular drawn from the origin to this line makes an angle of 45^ with the positive X-axis, then the equation of line is....

Options

  1. Ax + y = 7
  2. Bx + y = 7 2
  3. Cx + y = 2
  4. Dx + y = 2

Correct answer

B. x + y = 7 2

Step-by-step solution

Let the equation of the line in normal form be x + y = p . Given = 45^ , the equation becomes x 45^ + y 45^ = p , which simplifies to x + y = p 2 . The x-intercept is a = p 2 and the y-intercept is b = p 2 . The area of the triangle formed with the coordinate axes is 1 2 ab = 49 . Substituting the intercepts, we get 1 2 (p 2 )(p 2 ) = 49 . This gives p^2 = 49 , so p = 7 (since perpendicular distance p > 0 ). Therefore, the equation of the line is x + y = 7 2 . Answer: x + y = 7 2

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