question_answer

The number of equilateral triangles with \[y=\sqrt{3}(x-1)+2\] and \[y=-\sqrt{3x}\] as two of its sides is

A) 0

B) 1

C) 2

D) None of these

Correct Answer: D

Solution :

[d] The sides given are \[y=\sqrt{3}(x-1)+2\] and \[y=-x.\] Lines are at an angle \[60{}^\circ \] to each other. Now any line parallel to obtuse angle bisector will make equilateral triangle with these lines as its two sides. Therefore, infinitely many lines.