Straight Lines

Let A(a, b), B(3, 4) and C(-6,-8) respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point P(2a+3, 7b+5) from the line 2x+3y-4=0 measured parallel to the line x-2y-1=0 is

1. 17 56
2. 15 57
3. 17 57
4. 517

Let A(-2,-1), B(1,0), C( , ) and D( , ) be the vertices of a parallelogram ABCD. If the point C lies on 2x-y=5 and the point D lies on 3x-2y=6, then the value of | + + + | is equal to .

A line passing through the point A(9,0) makes an angle of 30 with the positive direction of x-axis. If this line is rotated about A through an angle of 15 in the clockwise direction, then its equation in the new position is :

1. y 3+2+x=9
2. x 3+2+y=9
3. x 3-2+y=9
4. y 3-2+x=9

If x2-y2+2hxy+2gx+2fy+c=0 is the locus of a point, which moves such that it is always equidistant from the lines x+2y+7=0 and 2x-y+8=0, then the value of g+c+h-f equals

1. 8
2. 14
3. 29
4. 6

Let (5, a4 ) be the circumcenter of a triangle with vertices A(a,-2), B(a, 6) and C ( a4,-2 ). Let denote the circumradius, denote the area and denote the perimeter of the triangle. Then + + is

1. 60
2. 62
3. 53
4. 30

In a ABC, suppose y=x is the equation of the bisector of the angle B and the equation of the side AC is 2x-y=2. If 2AB=BC and the points A and B are respectively (4,6) and ( , ), then +2 is equal to

1. 42
2. 39
3. 48
4. 45

Let A be the point of intersection of the lines 3x+2y=14, 5x-y=6 and B be the point of intersection of the lines 4x+3y=8, 6x+y=5. The distance of the point P(5,-2) from the line AB is

1. 132
2. 8
3. 52
4. 6

The distance of the point (2,3) from the line 2x-3y+28=0, measured parallel to the line 3x-y+1=0, is equal to

1. 3+4 2
2. 6 3
3. 4+6 3
4. 4 2

The portion of the line 4x+5y=20 in the first quadrant is trisected by the lines L1 and L2 passing through the origin. The tangent of an angle between the lines L1 and L2 is :

1. 3041
2. 85
3. 25
4. 2541

Let R be the interior region between the lines 3x-y+1=0 and x+2y-5=0 containing the origin. The set of all values of a, for which the points (a2,a+1 ) lie in R, is :

1. (-3,0) ( 23,1 )
2. (-3,0) ( 13,1 )
3. (-3,-1) ( 13,1 )
4. (-3,-1) (- 13,1 )