Question

The straight line passing through the point of intersection of the straight lines x – 3y + 1 = 0 and 2x + 5y – 9 = 0 and having infinite slope and at a distance 2 unit from the origin has the equation

Solution

Correct option is

x = 2

Any line through the intersection of the given line is

      P + λQ = 0

or  (x – 3y +1) + λ(2x + 5– 9) = 0

Its slope will be infinite if it is perpendicular to x-axis i.e. parallel to y-axis.

Hence the coefficient of y will be zero.

or                .

Putting for λ the line is x = 2 clearly its distance from (0, 0) is 2.

SIMILAR QUESTIONS

Q1

The equation to the side of a triangle are x – 3y = 0, 4x + 3= 5 and 3x + y = 0. The line 3x – 4y = 0 passes through 

Q2

One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is

Q3

A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 is

Q4

Let P = (–1, 0), Q = (0, 0) and  be three points. Then the equation of the bisector of the angle PQR is

Q5

Area of Δ formed by line x + y = 3 and  bisectors of pair of straight lines x2 – y2 +2y = 1is

Q6

The equation of the straight line which passes through the point (1, –2) and cuts off equal intercepts from the axes will be

Q7

The three lines 3x + 4y + 6 = 0,  and 4x + 7y + 8 = 0 are

Q8

The line (p + 2q)x + (p – 3q)y = p – q for different values of p and qpasses through the point

Q9

The locus of the mid-point of te portion intercepted between the axes by the line  where is constant is

Q10

shifting of origin (0, 0) to (h, k)

                        

                  Rotation of axes through an angle θ.

                          

1:- by rotating the axes through an angle θ the equation xy – y2 – 3+ 4 = 0 is transformed to the from which does not contain the term of xy then  ….