Q: 23 Prove that the product of the lengths of the perpendiculars drawn from the points and to the line is .
Q : 24 A person standing at the junction (crossing) of two straight paths represented by the equations and wants to reach the path whose equation is in the least time. Find equation of the path that he should follow.
Q : 22 A ray of light passing through the point reflects on the -axis at point and the reflected ray passes through the point . Find the coordinates of .
Q : 21 Find equation of the line which is equidistant from parallel lines and .
Q: 20 If the sum of the perpendicular distances of a variable point from the lines and is always . Show that must move on a line.
Q : 19 If the lines and are equally inclined to the line , find the value of .
Q : 18 Find the image of the point with respect to the line assuming the line to be a plane mirror.
Q : 17 The hypotenuse of a right angled triangle has its ends at the points and Find an equation of the legs (perpendicular sides) of the triangle.
Q: 16 Find the direction in which a straight line must be drawn through the point so that its point of intersection with the line may be at a distance of units from this point.
Q : 15 Find the distance of the line from the point along the line .
Q : 14 In what ratio, the line joining and is divided by the line ?
Q : 13 Show that the equation of the line passing through the origin and making an angle
with the line is .
Q: 12 Find the equation of the line passing through the point of intersection of the lines and that has equal intercepts on the axes.
Q: 11 Find the equation of the lines through the point which make an angle of with the line .
Q : 10 If three lines whose equations are and are concurrent, then show that .
Q : 9 Find the value of so that the three lines and may intersect at one point.
Q : 8 Find the area of the triangle formed by the lines and .
Q : 7 Find the equation of a line drawn perpendicular to the line
through the point, where it meets the -axis.
Q : 6 Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines and .
Q : 5 Find perpendicular distance from the origin to the line joining the points and .