HARD
JEE Advanced
IMPORTANT
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The centroid of an equilateral triangle is (0,0) . If two vertices of the triangle lie on x+y=22, then one of them will have its coordinates as

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Important Questions on Straight Line and Pair of Straight Lines

HARD
JEE Advanced
IMPORTANT
ABC is an equilateral triangle such that the vertices B and C lie on two parallel lines at a distance 6. If A lies between the parallel lines at a distance 4 from one of them, then the length of a side of the equilateral triangle is
HARD
JEE Advanced
IMPORTANT
If the straight lines a1x+b1y+c1=0,a1x+b1y+c2=0,a2x+b2y+d1=0 and a2x+b2y+d2=0 are the sides of rhombus, then
HARD
JEE Advanced
IMPORTANT
A straight line L1 makes angle tan-143 with the parallel lines 3 x-4 y-24=0 and 3 x-4 y-12=0 If L1 makes an intercept of 3 units with these parallel lines, then the equation L1 may be given as
HARD
JEE Advanced
IMPORTANT
The vertices of a ΔOBC are O0,0, B-3,-1 and C(-1,-3). The equation of a line parallel to BC and intersecting sides OB and OC whose distance from the origin is 12, is
MEDIUM
JEE Advanced
IMPORTANT
The image of the point P3,5 with respect to the line y=x is the point Q, R is the image of Q with respect to the line y=0 is the point Ra,b, then a,b is equal to
MEDIUM
JEE Advanced
IMPORTANT
The equation of the diagonal through origin of the quadrilateral formed by the line x=0, y=0, x+y-1=0 and 6 x+y-3=0 is
HARD
JEE Advanced
IMPORTANT
Consider a family of straight lines x+y+λ2x-y+1=0. Equation of the straight line belonging to this family that is farthest from 1,-3 is
HARD
JEE Advanced
IMPORTANT
A family of lines is given by 1+2λx+1-λy+λ=0, λ being the parameter. The line belonging to this family at the maximum distance from the point 1,4 is