Condition of a line whose catches on the axes are an and b is \[\mathbf{x}/\mathbf{a}\text{ }+\text{ }\mathbf{y}/\mathbf{b}\text{ }=\text{ }\mathbf{1}\] \[\mathbf{bx}\text{ }+\text{...
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.
Leave AD alone the height of triangle ABC from vertex A. In this way, AD is opposite to BC Given: Vertices \[\mathbf{A}\text{ }\left( \mathbf{2},\text{ }\mathbf{3} \right),\text{...
If p and q are the lengths of perpendiculars from the origin to the lines x cos θ − y sin θ = k cos 2θ and x sec θ + y cosec θ = k, respectively, prove that p2 + 4q2 = k2
Given: The equations of given lines are x cos θ – y sin θ = k cos 2θ …………………… (1) x sec θ + y cosec θ = k ……………….… (2) Perpendicular distance (d) of a line Ax + By + C = 0 from a point (x1, y1) is...
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.
Given: The opposite from the beginning meets the given line at \[\left( \text{ }\mathbf{1},\text{ }\mathbf{2} \right).\] The condition of line is \[\mathbf{y}\text{ }=\text{ }\mathbf{mx}\text{...
Find the coordinates of the foot of perpendicular from the point (–1, 3) to the line 3x – 4y – 16 = 0.
Allow us to consider the co-ordinates of the foot of the opposite from (- 1, 3) to the line \[\mathbf{3x}\text{ }\text{ }\mathbf{4y}\text{ }\text{ }\mathbf{16}\text{ }=\text{ }\mathbf{0}\text{...
Find the equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2).
Given: The right bisector of a line section divides the line fragment at \[\mathbf{90}{}^\circ .\] End-points of the line portion AB are given as \[\mathbf{A}\text{ }\left( \mathbf{3},\text{...
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.
Given\[:\text{ }\mathbf{m1}\text{ }=\text{ }\mathbf{2}\] Leave the slant of the principal line alone m1 What's more, left the incline of the other line alone m2. Point between the two lines is...
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.
Let the slant of line \[\mathbf{Ax}\text{ }+\text{ }\mathbf{By}\text{ }+\text{ }\mathbf{C}\text{ }=\text{ }\mathbf{0}\] be m \[\mathbf{Ax}\text{ }+\text{ }\mathbf{By}\text{ }+\text{...
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.
Let the incline of the line going through (h, 3) and (4, 1) be m1 Then, at that point, \[\mathbf{m1}\text{ }=\text{ }\left( \mathbf{1}-\mathbf{3} \right)/\left( \mathbf{4}-\mathbf{h} \right)\text{...
Find angles between the lines √3x + y = 1 and x + √3y = 1.
Given: The lines are \[\surd \mathbf{3x}\text{ }+\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{1}\text{ }\mathbf{and}\text{ }\mathbf{x}\text{ }+\text{ }\surd \mathbf{3y}\text{ }=\text{ }\mathbf{1}\]...
Find equation of the line perpendicular to the line x – 7y + 5 = 0 and having x intercept 3.
Given: The condition of line is \[\mathbf{x}\text{ }\text{ }\mathbf{7y}\text{ }+\text{ }\mathbf{5}\text{ }=\text{ }\mathbf{0}\] Thus, \[\mathbf{y}\text{ }=\text{ }\mathbf{1}/\mathbf{7x}\text{...
Find equation of the line parallel to the line 3x − 4y + 2 = 0 and passing through the point (–2, 3).
Given: The line is \[\mathbf{3x}\text{ }\text{ }\mathbf{-4y}\text{ }+\text{ }\mathbf{2}\text{ }=\text{ }\mathbf{0}\] In this way, \[\mathbf{y}\text{ }=\text{ }\mathbf{3x}/\mathbf{4}\text{ }+\text{...
Find the distance between parallel lines (i) 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0 (ii) l(x + y) + p = 0 and l (x + y) – r = 0
\[\left( \mathbf{i} \right)\text{ }\mathbf{15x}\text{ }+\text{ }\mathbf{8y}\text{ }\text{ }\mathbf{34}\text{ }=\text{ }\mathbf{0}\text{ }\mathbf{and}\text{ }\mathbf{15x}\text{ }+\text{...
Find the points on the x-axis, whose distances from the line x/3 + y/4 = 1 are 4 units.
Given: The condition of line is \[\mathbf{x}/\mathbf{3}\text{ }+\text{ }\mathbf{y}/\mathbf{4}\text{ }=\text{ }\mathbf{1}\] \[\mathbf{4x}\text{ }+\text{ }\mathbf{3y}\text{ }=\text{ }\mathbf{12}\]...
Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).
Given: The condition of the line is \[\mathbf{12}\left( \mathbf{x}\text{ }+\text{ }\mathbf{6} \right)\text{ }=\text{ }\mathbf{5}\left( \mathbf{y}\text{ }\text{ }\mathbf{2} \right).\]...
Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis. (iii) x – y = 4
\[\left( \mathbf{iii} \right)\text{ }\mathbf{x-}\text{ }\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{4}\] Given: The condition is \[\mathbf{x-}\text{ }\text{ }\mathbf{y}\text{ }+\text{...
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
(i) x – √3y + 8 = 0 Given: The condition is \[\mathbf{x}\text{ }\text{ }\surd \mathbf{3y}\text{ }+\text{ }\mathbf{8}\text{ }=\text{ }\mathbf{0}\] Condition of line in typical structure is given...
Reduce the following equations into intercept form and find their intercepts on the axes. (iii) 3y + 2 = 0
\[\left( \mathbf{iii} \right)\text{ }\mathbf{3y}\text{ }+\text{ }\mathbf{2}\text{ }=\text{ }\mathbf{0}\] Given: The condition is \[\mathbf{3y}\text{ }+\text{ }\mathbf{2}\text{ }=\text{...
Reduce the following equations into intercept form and find their intercepts on the axes. (i) 3x + 2y – 12 = 0 (ii) 4x – 3y = 6
\[\left( \mathbf{i} \right)\text{ }\mathbf{3x}\text{ }+\text{ }\mathbf{2y}\text{ }\text{ }\mathbf{-12}\text{ }=\text{ }\mathbf{0}\] Given: The condition is \[\mathbf{3x}\text{ }+\text{...
Reduce the following equations into slope – intercept form and find their slopes and the y – intercepts.(iii) y = 0
\[\left( \mathbf{iii} \right)\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{0}\] Given: The condition is \[\mathbf{y}\text{ }=\text{ }\mathbf{0}\] Slant – catch structure is given...
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
As indicated by the inquiry, \[~\left( \mathbf{i} \right)\text{ }\mathbf{x}\text{ }+\text{ }\mathbf{7y}\text{ }=\text{ }\mathbf{0}\] Given: The condition is \[\mathbf{x}\text{ }+\text{...