Chapter 9
Find the values of k for which the line ( k-3) x - (4 - k2) y + k2 -7k + 6 = 0 is (a) Parallel to the x-axis, (b) Parallel to the y-axis, (c) Passing through the origin.
Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and - 6, respectively.
What are the points on the y-axis whose distance from the line 13 4 x y+ = is 4 units.
Find perpendicular distance from the origin to the line joining the points (cosθ, sin θ) and (cos φ, sin φ).
Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines x - 7y + 5 = 0 and 3x + y = 0.
Find the equation of a line drawn perpendicular to the line 1 = +y x through the point, where it meets the y-axis.
Find the area of the triangle formed by the lines y - x = 0, x + y = 0 and x - k = 0.
Find the value of p so that the three lines 3x + y - 2 = 0, px + 2 y - 3 = 0 and 2x - y - 3 = 0 may intersect at one point.
If three lines whose equations are y = m1x + c1, y = m2x + c2 and y = m3x + c3 are concurrent, then show that m1(c2 - c3) + m 2 (c3 - c 1) + m3 (c1 - c 2) = 0.
Find the equation of the lines through the point (3, 2) which make an angle of 45o with the line x - 2y = 3.
Find the equation of the line passing through the point of intersection of the lines 4x + 7y - 3 = 0 and 2x - 3y + 1 = 0 that has equal intercepts on the axes.
Show that the equation of the line passing through the origin and making an angle θ with the line y mx c is y x m m= + = ± tan ‚ tan ‚ 1∓ .
In what ratio, the line joining (-1, 1) and (5, 7) is divided by the line x + y = 4?
Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x - y = 0.
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 of 3 units from this point.
The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (- 4, 1). Find an equation of the legs (perpendicular sides) of the triangle which are parallel to the axes.
Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the line to be a plane mirror.
If the lines y = 3x +1 and 2 y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.
If sum of the perpendicular distances of a variable point P ( x, y) from the lines x + y - 5 = 0 and 3x - 2y +7 = 0 is always 10. Show that P must move on a line.
Find equation of the line which is equidistant from parallel lines 9x + 6y - 7 = 0 and 3x + 2y + 6 = 0.
A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.
Prove that the product of the lengths of the perpendiculars drawn from the points ( ) 2 2 0a b ,− and ( ) 2 2 0a b ,− − to the line 2cosθ sin θ 1isx y ba b + = .
A person standing at the junction (crossing) of two straight paths represented by the equations 2x - 3y + 4 = 0 and 3x + 4y - 5 = 0 wants to reach the path whose equation is 6x - 7y + 8 = 0 in the least time. Find equation of the path that he should follow.