Question

Find the equation of the straight line through the point P(ab) parallel to the lines . Also find the intercepts made by it on the axes.

Solution

Correct option is

2a and 2b

 

Let the line 

meets the axes in A and B respectively. 

 

So that 

        OA = aOB = b    

Let the required parallel line meet in A’ and B’ respectively, so thet  

       OA’ = a’ and OB’ = b’  

∴ Equation of required line is  

          

Since ∆’s OAB and OAB’ are similarly, then  

        

Substituting these values in eq. (i) then 

          

It passes through (ab) then 

          

From (ii) required equation is

           

Evidently intercepts on the axes are 2a  and 2b.

SIMILAR QUESTIONS

Q1

Find the equation of the straight line bisecting the segment joining the points (5, 3) and (4, 4) and making an angle of 45o with the positive direction of x-axis.

Q2

Find the equation of the right bisector of the line joining (1, 1) and (3, 5).

Q3

Find the equation to the straight line joining the points .

Q4

 

Let ABC be a triangle with A(–1, –5), B(0, 0) and C(2, 2) and let D be the middle point of BC. Find the equation of the perpendicular drawn from Bto AD.  

 

Q5

The vertices of a triangle are A(10, 4), B(–4, 9) and C(–2, –1). Find the equation of the altitude through A.

Q6

Find the equations of the medians of a triangle, the coordinates of whose vertices are (–1, 6), (–3, –9) and (5, –8).

Q7

Find the ratio in which the line segment joining the points (2, 3) and (4, 5) is divided by the line joining (6, 8) and (–3, –2).

Q8

Find the equation of the line through (2, 3) so that the segment of the line intercepted between the axes is bisected at this point.

Q9

 

Find the equation to the straight line which passes through the points (3, 4) and having intercepts on the axes: 

1. equal in magnitude but opposite in sign 

2. such that their sum is 14

Q10

The length of perpendicular from the origin to a line is 9 and the line makes an angle of 120o with the positive direction of y-axis. Find the equation of the line.