Question

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

Solution

Correct option is

2

Eliminating y, the x-coordinates of point of intersection is given by

        

Because x is also an integral

∴  3 + 4= 1, –1, 5 or –5

or       4= –2,  –4,2, –8

 

In all four values but integral values of m are only two i.e. –1 and –2.

SIMILAR QUESTIONS

Q1

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

               

Q2

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

Q3

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:

Q4

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 and y)

Q5

If x1x2x3 as well as y1y2y3 are in G.P. with the same common ratio, then the points (x1y1), (x2y2) and (x3y3)

Q6

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

Q7

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

Q8

Consider three points

              ,

               and

              , then

Q9

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

Q10

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