LONG ANSWER TYPE QUESTIONS
1) The slope of a line is double the slope of another line . If the tangent
of the angle between them is 1/3 . Find the slope of the lines .
2) Find the distance of the line 4x – y = 0 from the point P(4 , 1 )
measured along the line making an angle of 1350 with the X –axis .
3) Find the equation of the line which satisfying the conditions
i) intersecting the X-axis at a distance of 3 units to the left of Origin
with slope -2
4) Find the equation of the line passing through the point ( 2 , 2 ) and
cutting off intercepts on the axes whose sum is 9 .
5)Find the equation of the line through the point ( 0 , 2 ) making an
angle 2π/3 with the positive X-axis . Also find the equation of the
line parallel to it and crossing the Y axis at a distance of 2 units
below the origin.
6) Reduce the equation x - y = 4 into slope intercept form . Find their
perpendicular distances from the origin and angle between
perpendicular and the positive X-axis .
7) A line is such that its segment between the lines 5x – y + 4 = 0 and
3x + 4y -4 = 0 is bisected at the point ( 1 , 5 ) . Obtain its equation.
8) In a triangle ABC with vertices A( 2,3 ) B( 4 , -1 ) and C ( 1 , 2 ) , find
the equation and length of altitude from the vertex A .
9) Show that the locus of the mid-point of the distance between the
axes of the variable line x cosa + y sina = p is
where p is a constant.
10) If the slope of a line passing through the point A(3, 2) is ¾ then
find points on the line which are 5 units away from the point A.
11) Find the equation to the straight line passing through the point of
intersection of the lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and
perpendicular to the line 3x – 5y + 11 = 0.
12) A ray of light coming from the point (1, 2) is reflected at a point A on
the x-axis and then passes through the point (5, 3). Find the
coordinates of the point A.
13) If one diagonal of a square is along the line 8x – 15y = 0 and one of
its vertex is at (1, 2), then find the equation of sides of the square
passing through this vertex.
