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9. straight line — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS9. straight line1 Mark
MCQ
$ABC$ is a variable triangle such that $A$ is $(1, 2)$ , $B$ and $C$ lie on line $y = x + \lambda $(where $\lambda $ is a variable), then locus of the orthocenter of triangle $ABC$ is
  • A
    $(x -1)^2 + y^2 = 4$
  • ✓
    $x + y = 3$
  • C
    $2x -y = 0$
  • D
    none of these
✓

Answer

Correct option: B.
$x + y = 3$
b
As altitude from $A$ is fixed and orthocentre lies on altitude hence $x + y = 3$ is required locus.

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