Let L1 be a straight line passing through the origin and L2 be the straight line x +y =1. If the intercepts made by the circle x2 + y2 –x +3y=0 on L1 and L2 are equal , then which of the following equations can represent L1?
X+ y =0
X –y=0
X +7y=0
X –7y=0
2 and 3
1 and 4
Area of the triangle formed by the line x +y=3 and angle bisectors of the pair of straight lines x2 – y2 + 2y=1 is
2 sq. units
4 sq. units
6 sq. units
8 sq. units
Let PS be the median of the triangle with vertices P(2,2), Q(6-1) and R(7,3). The equation of the line passing through (1-1) and parallel to PS is
2x-9y-7 =0
2x-9y-11 =0
2x+ 9y-11=0
2x+9y+7=0
Area of the parallelogram formed by the lines y= mx, y=mx+1, y=nx and y=nx +1 equals
|m+n|/(m-n)2
2/|m+n|
1/(|m+n|)
1/(|m-n|)
If the vertices P, Q, R of a triangle PQR are rational points, which of the following points of the triangle PQR is always rational point(s)?
Circumcentre
incentre
centre
Orthocentre
If (P(1,2), Q(4,6), R(5,7) and S(a, b) are the vertices of a parallelogram PQRS, then
a=2, b=4
a=3, b=4
a=2, b=3
a=3, b=5
The point (-a,-b). (0,0), (a, b) and (a2, ab) are:
Collinear
Vertices of a parallelogram
Vertices of a rectangle
None of these
The straight lines x+y =0, 3x +y-4=0,x+3y-4=0 form a triangle which is
isosceles
equilateral
right angled
none of these
If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is
Square
Circle
Straight
Two intersecting lines
Let PQR be a right angled isosceles triangle, right angled at P(2,1). If equation of the line QR is 2x+ Y=3, then the equation representing the pair of lines PQ and PR is
3x2-3y2+8xy+20x+10y+25=0
3x2-3y2+8xy-20x+10y+25=0
3x2-3y2+8xy+10x+15y+20=0
3x2 -3y2-8xy-10x-15y-20=0