Question:
A square is inscribed in a circle x2 + y2 + 2x + 2y + 1 =0 and its sides are parallel to coordinate axes. Which one of the following is a vertex of the square?
A square is inscribed in a circle x2 + y2 + 2x + 2y + 1 =0 and its sides are parallel to coordinate axes. Which one of the following is a vertex of the square?
Options:
- a) (-2, 2)
- b) (-2, -2)
- c) 1 2 1 1 2 ,
- d) None of the above
- a) (-2, 2)
- b) (-2, -2)
- c) 1 2 1 1 2 ,
- d) None of the above
correct answer : c)
Explanation:
2
a
2
a
Equation of circle is
x2 + y2 + 2x + 2y + 1 = 0
\ centre = (-1, -1)
Radius = 11 1+- = 1
Diagonal = diameter
2a = 2 Þ a = 2
Since the sides of the square are parallel to the
co-ordinate axes, the vertices can be found by
moving a
2
units from the centre along the axes.
\ One of the vertices is
-+ –
1 1
2
1 1
2
,
2
a
2
a
Equation of circle is
x2 + y2 + 2x + 2y + 1 = 0
\ centre = (-1, -1)
Radius = 11 1+- = 1
Diagonal = diameter
2a = 2 Þ a = 2
Since the sides of the square are parallel to the
co-ordinate axes, the vertices can be found by
moving a
2
units from the centre along the axes.
\ One of the vertices is
-+ –
1 1
2
1 1
2
,