Question 1:Reduce the following equations into slope - intercept form and find their slopes and the y - intercepts. (i) x + 7y = 0, (ii) 6x + 3y – 5 = 0, (iii) y = 0.
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Question 2:Reduce the following equations into intercept form and find their intercepts on the axes. (i) 3x + 2y – 12 = 0, (ii) 4x – 3y = 6, (iii) 3y + 2 = 0.
Question 3:Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis. (i) x – 3y + 8 = 0, (ii) y – 2 = 0, (iii) x – y = 4.
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Question 4:Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).
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Question 5:Find the points on the x-axis, whose distances from the line 1 3 4 x y + = are 4 units.
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Question 6:Find the distance between parallel lines (i) 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0 (ii) l (x + y) + π = 0 and l (x + y) – r = 0.
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Question 7:Find equation of the line parallel to the line 3x − 4y + 2 = 0 and passing through the point (–2, 3).
Question 8:Find equation of the line perpendicular to the line x – 7y + 5 = 0 and having x intercept 3.
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Question 9:Find angles between the lines 3x + y = 1and x + 3y = 1.
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Question 10:The line through the points (h, 3) and (4, 1) intersects the line 7x − 9y −19 = 0. at right angle. Find the value of h.
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Question 11:Prove that the line through the point (x1, y1) and parallel to the line Ax + By + C = 0 is A (x –x1) + B (y – y1) = 0.
Question 12:Two lines passing through the point (2, 3) intersects each other at an angle of 60o. If slope of one line is 2, find equation of the other line.
EXERCISE 10.31. Reduce the following equations int
Question 13:Find the equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2).
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Question 14:Find the coordinates of the foot of perpendicular from the point (–1, 3) to the line 3x – 4y – 16 = 0.
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Question 15:The perpendicular from the origin to the line y = mx + c meets it at the point (–1, 2). Find the values of m and c.
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Question 16:If π and q are the lengths of perpendiculars from the origin to the lines x cos − ysin = k cos2 and x sec q + y cosec q = k, respectively, prove that p2 + 4q2 = k2.
Question 17:In the 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.
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Question 18:If π is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that . 1 1 1 2 2 2 p a b
