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1.
The equation of the bisectors of the angles between the lines 
are
are
2.
Consider the family of lines 
and
equation of the straight line that belongs to both the families is
and3.
A straight line passing through 
(3, 1) meet the coordinate axes at 
and 
. It is given that distance of this straight line from the origin ‘O’ is maximum. Area of 
is equal to
(3, 1) meet the coordinate axes at and . It is given that distance of this straight line from the origin ‘O’ is maximum. Area of is equal to
4.
The lines represented by the equation 
are
are
5.
If the bisectors of angles represented by 
and 
are same, then
and are same, then
6.
If is a point 
on the line 
such that and the point 
are on the opposite sides of the line 
, then
is a point on the line such that and the point are on the opposite sides of the line , then
7.
A point equidistant from the lines 
and 
is
and is
8.
The straight line 
intersects the 
-axis and 
-axis at and respectively. Then the distance 
where 
is the centre of the in-circle of 
where is the origin, is equal to
intersects the -axis and -axis at and respectively. Then the distance where is the centre of the in-circle of where is the origin, is equal to
9.
Let 
be a right angled isosceles triangle, right angled at 
. If the equation of the line 
is 
, then the equation representing the pair of lines 
and 
is
be a right angled isosceles triangle, right angled at . If the equation of the line is , then the equation representing the pair of lines and is
10.
A point moves in the 
-plane such that the sum of its distance from two mutually perpendicular lines is always equal to 3. The area of the locus of the point is
-plane such that the sum of its distance from two mutually perpendicular lines is always equal to 3. The area of the locus of the point is