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

None of these

3a and 4b

a and b

2a and 2b
diffcult
Solution
2a and 2b
Let the line
meets the axes in A and B respectively.
So that
OA = a, OB = 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 âˆ†’s OAB and OA’B’ are similarly, then
.
Substituting these values in eq. (i) then
It passes through (a, b) then
.
From (ii) required equation is
Evidently intercepts on the axes are 2a and 2b.
SIMILAR QUESTIONS
Find the equation of the straight line bisecting the segment joining the points (5, 3) and (4, 4) and making an angle of 45^{o} with the positive direction of xaxis.
Find the equation of the right bisector of the line joining (1, 1) and (3, 5).
Find the equation to the straight line joining the points .
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.
The vertices of a triangle are A(10, 4), B(–4, 9) and C(–2, –1). Find the equation of the altitude through A.
Find the equations of the medians of a triangle, the coordinates of whose vertices are (–1, 6), (–3, –9) and (5, –8).
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).
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.
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
The length of perpendicular from the origin to a line is 9 and the line makes an angle of 120^{o} with the positive direction of yaxis. Find the equation of the line.