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
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|)
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
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
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
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