HARD
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The equation of the image of line y=x with respect to the line mirror 2x-y=1 is

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Important Questions on Straight Lines

MEDIUM
If the family of straight lines ax+by+c=0, where 2a+3b=4c is concurrent at the point Pl, m, then the foot of the perpendicular drawn from P to the line x+y+1=0 is
EASY
The length of perpendicular from the point acosα,asinα upon the straight line y=xtanα+c, c>0 is
MEDIUM
The length of the perpendicular from 1,-2 to the line 12x+5y+63=0 is
MEDIUM
If the points 1, 1, λ & (-3, 0, 1), are equidistant from the plane, 3x+4y-12z+13=0, then λ satisfies the equation:
EASY
Which one of the following points lies on the straight line x-12=y+14=z-2-2?
EASY
The polar coordinate of a point P is 2, -π4. The polar coordinate of the point Q which is such that line joining PQ is bisected perpendicularly by the initial line, is
HARD
A ray of light is projected from the origin at angle of 60° with the positive direction of x-axis towards the line, y=2, which gets reflected from the point, (α,2). Then the distance of the reflected ray of light from the point (2,2) is
HARD
A ray of light passing through the point 1, 2 is reflected on the x -axis at a point P and passes through the point 5, 3 then the abscissa of a point P is
MEDIUM
The set of all possible values of θ in the interval 0,π for which the points 1, 2 and sinθ, cosθ lie on the same side of the line x+y=1 is?
MEDIUM
Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point-1, -4 in the line is :
EASY
The foot of the perpendicular drawn from the point (1, 8, 4) on the line joining the point (0, -11, 4) and (2,-3,1) is
MEDIUM

If Q(0,-1,-3) is the image of the point P in the plane 3x-y+4z=2 and R is the point (3,-1,-2), then the area (in sq. units) of ΔPQR is

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MEDIUM
Let S be a subset of the plane defined by S=x,y:|x|+2|y|=1. Then, the radius of the smallest circle with centre at the origin and having non-empty intersection with S is
MEDIUM
Let a0, b0, c be three real numbers and Lp,q=ap+bq+ca2+b2,  p, qR. If L23,13+L13,23+L(2,2)=0, then the line ax+by+c=0 always passes through the fixed point
MEDIUM
If the point a, a falls between the lines x+y=4, then
HARD
If C is the reflection of A2, 4 in x-axis and B is the reflection of C in y-axis then AB is -
MEDIUM
The image of the point 3,5 in the line x-y+1=0, lies on :
MEDIUM

A ray of light coming from the point (2,23) is incident at an angle 30° on the line x=1 at the point A. The ray gets reflected on the line x=1 and meets x -axis at the point B. Then, the line AB passes through the point
 

EASY
The coordinates of the foot of the perpendicular from the point 2,3 on the line x+y-11=0 is
MEDIUM
A point on the straight line, 3x+5y=15 which is equidistant from the coordinate axes will lie only in: