The Number Of Integral Values Of m, For Which The x-coordinates Of The Point Of Intersection Of The Lines 2x + 4y = 9 And  Y = Mx + 1 Is Also An Integral Is

The line joining the point  is produced to the point L(x, y) so that AL : LB = b : a, then 

The vertex of a triangle are the points A(–36, 7), B(20, 7) and C(0, –8), If G and I be the centoid and in center of the triangle, then GI is equal to

If a, b, c are relation by 4a² + 9b² – 9c² + 12ab = 0 then the greatest distance between any two lines of the family of lines

ax + by + c = 0 is:

Triangle is formed by the coordinates (0, 0), (0, 21) and (21, 0). Find the numbers of integral coordinates strictly inside the triangle (integral coordinates of both x and y)

If x₁, x₂, x₃ as well as y₁, y₂, y₃ are in G.P. with the same common ratio, then the points (x₁, y₁), (x₂, y₂) and (x₃, y₃)

Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are

If a, b, c are all unequal and different from one and the points  are collinear then ab + bc + ca =

Consider three points

              ,

               and

              , then

The lines p(p² + 1)x – y + q = 0 and (p² + 1)² x + (p² + 1)y + 2q = 0 are perpendicular to a common line for

Let PS be the median of the triangle with vertices P(2, 2), Q(6, –1) andR(7, 3). The equation of the line passing through

(1, –1) and parallel toPS is