## Question

Find the direction in which a straight line must be drawn through the point (1, 2) so that its point of intersection with the line

*x* + *y* = 4 may be at a distance from this point.

### Solution

15^{o}, 75^{o}

Let the straight line makes an angle θ with the positive direction of x-axis.

∴ Equation of the line through (1, 2) in parametric form is

Since the point lies on the line

*x* + *y* = 4

for *n* = 0,

= 15^{o}, 75^{o}.

#### SIMILAR QUESTIONS

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

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.

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 y-axis. Find the equation of the line.

Find the equation of the straight line on which the perpendicular from origin makes an angle of 30^{o} with x-axis and which forms a triangle of area sq. units with the coordinates axes.

Find the measure of the angle of intersection of the lines whose equations are 3*x* + 4*y* + 7 = 0 and 4*x* – 3*y* + 5 = 0.

Find the angle between the lines

where *a* > *b* > 0.

The slope of a straight line through *A*(3, 2) is 3/4. Find the coordinates of the points on the line that are 5 units away from *A*.

Find the distance of the point (2, 3) from the line 2*x* – 3*y* + 9 = 0 measured along the line 2*x* – 2*y* + 5 = 0.