Question

Given the family of lines a(2x + y + 4) + b(x – 2y – 3) = 0. The number of lines belonging to the family at a distance  from any point (2, –3) is

Solution

Correct option is

1

 

, the given family is

          

Its distance from (2, –3) is 

or 

or 

or 

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

Consider three points

              ,

               and

              , then

Q5

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

Q6

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

Q7

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

Q8

Let PQR be a right angled isosceles triangle, right angled at P(2, 1). If the equation of the line QR is 2x + y = 3, then the equation representing the pair of lines PQ and PR is

Q9

The point (2, 1) is shifted through a distance  units measured parallel to the line x + y = 1 in the direction of decreasing ordinates to reach Q.The image of Q w.r.t. given line is

Q10

 

Given four lines with equations x + 2y – 3 = 0, 3x + 4y – 7 = 0,

2x + 3y – 4 = 0, 4x + 5y – 6 = 0, then