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Unit 5: Equations of Straight Lines

7. Find the equation whose distance from origin is 4 and angles is 15° in positive direction Notes
(a) x cos 15° + y sin 15° = 4
(b) x sin 15 + y cos 15° = 4
-1
(c) x sin 15 + y cos 15° = 4
-1
(d) x sin 15° + y cos 15° = 4
-1
-1
8. Distance between two parallel lines 3x 4y + 7 = 0
(a) 2/3
(b) 2/4

(c) 2/5
(d) 2/6
9. Equation of slope - Intercept form of line is
(a) y = mx + c

2
(b) y = m x + cx
2
2
(c) y = m x + c
(d) y = m/2 x +c
10. Distance of the point (3, 5) from the line 3x 4y 26 = 0 is

(a) 3/5
(b) 4/3
(c) 3/4
(d) 5/3

5.9 Review Qustions

1. Find perpendicular distance from the origin of the line joining the points (cos , sin ) and
(cos , sin ).
2. Find the area of the triangle formed by the lines y x = 0, x + y = 0 and x k = 0.

3. 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.
4. If three lines whose equations are y = m x + c , y = m x + c and y = m x + c are concurrent,
1 1 1 2 3 3
then show that m (c c ) + m (c c ) + m (c c ) = 0.
1 2 3 2 3 1 3 1 2
o
5. Find the equation of the lines through the point (3, 2) which make an angle of 45 with the
line x 2y = 3.
6. Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be
a plane mirror.
7. 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.

8. 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.

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