11th Std Math Practical
Mathematics and Statistics (Arts and Science)
Answers (Solutions)
Practical No.5
5) Straight Lines
Practical Session No. 5 Straight Lines
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Practical Session No. 5 Straight Lines
(1) Show that the equation of the line passing through 𝐴𝐴(𝑥𝑥1,𝑦𝑦1) and parallel to the line 𝑎𝑎𝑎 +𝑏𝑏𝑏 +𝑐𝑐=0 is 𝑎𝑎(𝑥𝑥−𝑥𝑥1)+𝑏𝑏(𝑦𝑦−𝑦𝑦1)=0. Hence find the equation of the line passing through (1,1) and parallel to the line 15𝑥𝑥+8𝑦𝑦+1947=0.
(2) Show that the equation of the line having slope 𝑚𝑚 and making X - intercept 𝑑 is given by 𝑦𝑦=𝑚𝑚(𝑥𝑥−𝑑 ). Find the Y - intercept of this line.
(3) A line makes intercepts ℎ and 𝑘𝑘 on the co-ordinate axes. If 𝑝𝑝 is the length of the perpendicular drawn from the origin to the line then show that 1ℎ2+1𝑘𝑘2=1𝑝𝑝2.
(4) Show that there are two lines which pass through the point 𝐴𝐴(3,7) and the sum of whose intercepts on the co-ordinate axes is zero. Draw the rough sketch of these two lines.
(5) Find the number of lines which pass through the point 𝐵 (5 ,5) and the sum of whose intercepts on the co-ordinate axes is zero.
(6) Find the co-ordinates of the orthocenter of the triangle formed by lines2𝑥𝑥−𝑦𝑦−9=0, 𝑥𝑥−2𝑦𝑦+9=0 and 𝑥𝑥+𝑦𝑦−9=0.
खलील व्हिडीओ त उत्तरे व Solution मिळेल
Practical Session No. 5
Straight Lines
(1) Show that the equation of the line passing through 𝐴𝐴(𝑥𝑥1,𝑦𝑦1) and parallel to the line 𝑎𝑎𝑎 +𝑏𝑏𝑏 +𝑐𝑐=0 is 𝑎𝑎(𝑥𝑥−𝑥𝑥1)+𝑏𝑏(𝑦𝑦−𝑦𝑦1)=0. Hence find the equation of the line passing through (1,1) and parallel to the line 15𝑥𝑥+8𝑦𝑦+1947=0.
(2) Show that the equation of the line having slope 𝑚𝑚 and making X - intercept 𝑑 is given by 𝑦𝑦=𝑚𝑚(𝑥𝑥−𝑑 ). Find the Y - intercept of this line.
(3) A line makes intercepts ℎ and 𝑘𝑘 on the co-ordinate axes. If 𝑝𝑝 is the length of the perpendicular drawn from the origin to the line then show that 1ℎ2+1𝑘𝑘2=1𝑝𝑝2.
(4) Show that there are two lines which pass through the point 𝐴𝐴(3,7) and the sum of whose intercepts on the co-ordinate axes is zero. Draw the rough sketch of these two lines.
(5) Find the number of lines which pass through the point 𝐵 (5 ,5) and the sum of whose intercepts on the co-ordinate axes is zero.
(6) Find the co-ordinates of the orthocenter of the triangle formed by lines
2𝑥𝑥−𝑦𝑦−9=0, 𝑥𝑥−2𝑦𝑦+9=0 and 𝑥𝑥+𝑦𝑦−9=0.
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