If t1, t2, t3 are distinct, then the points are collinear if:
A and B are two fixed points. The vertex C of a Δ ABC moves such that cot A + cot B = constant. Locus of C is a straight line:
The number of integer values of m, for which the x-co-ordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer, is:
The vertices of a triangles are A (x1, x1 tan α), B (x2, x2 tan β) and C (x3,x3 tan γ). If the circumcentre of Δ ABC coincides with the origin and H (a, b) 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 p1, p2, p3 be the length perpendicular from the points
(m2, 2m), (mm’, m + m’) and (m’2, 2m’)
respectively on the line
The point (a2, a + 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 bisector of the acute angle between the line 3x + 4y = 11 and 12x – 5y = 2.