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rectangular cartensian co-ordinates — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSrectangular cartensian co-ordinates1 Mark
MCQ
Let $B C$ be a fixed line segment in the plane. The locus of a point $A$ such that the $\triangle A B C$ is isosceles, is (with finitely many possible exceptional points)
  • A
    a line
  • B
    a circle
  • C
    the union of a circle and a line
  • ✓
    the union of two circles and a line
✓

Answer

Correct option: D.
the union of two circles and a line
d
(d)

Given in $\triangle A B C, B C$ is fixed, $A$ is variable and $A B C$ is an isosceles triangle.

Case $I$ In $\triangle A B C$,

If $\quad A B=A C$

Then, locus of $A$ is perpendicular bisector of $B C$.

$\therefore$ Locus of $A$ is a straight line.

Case $II$ When $A B=B C$

$B C$ fixed $B(a, 0), C(0, a)$, locus of $A$ is $(x-a)^2+y^2=2 a^2$, which represents the equation of circle.

Similarly, when $A C=B C$ also locus of $A$ is circle.

$\therefore$ Locus of $A$ is the union of two circles and the lines.

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