A straight line drawn through point A (2, 1) making an angle π/4 with the +X-axis intersects another line x + 2y + 1= 0 in point B. Find the length AB.


Correct option is

Let AB = r  

From parametric form, the point B can be taken as:




As B lies on x + 2y + 1= 0, we have:    


Note that r is negative, as the point B lies below the point A.  



The vertices of a triangles are A (x1x1 tan α), B (x2x2 tan β) and C (x3,x3 tan γ). If the circumcentre of Δ ABC coincides with the origin and H (ab) be its orthocenter, then a/b is equal to:


A straight line L with negative slope passes through the point (8, 2) and cuts the positive coordinates axes at points P and Q. As L varies, the absolute minimum values of OP + OQ is (O is origin)




Consider the family of lines 

           (x + y – 1) + λ (2x + 3y – 5) = 0

and   (3x + 2y – 4) + µ (x + 2y – 6) = 0  

equation of a straight line that belongs to both the families is:


If p1p2p3 be the length perpendicular from the points

(m2, 2m), (mm’m + m’) and (m’2, 2m’)

respectively on the line  



The point (a2a + 1) is a point in the angle between the lines 3x – y + 1 = 0 and x + 2y – 5 = 0 containing origin. Then ‘a’ belongs to the interval. 


Find all points on x + y = 4 that lie at a unit distance from the line 4x + 3y– 10 = 0.


Find the equation of the obtuse angle bisector of the lines 12x – 5y + 7 = 0 and 3y – 4x – 1 = 0.


Find the bisector of the acute angle between the line 3x + 4y = 11 and 12x – 5y = 2. 


Find the equation of the locus of a moving point so that its distance from the point (1, 0) is always twice the distance from the point (0, –2).