Straight Lines — Class 11 solved problems

19 problems from this chapter, each solved step by step.

Let A(6,8), B(10cosα, -10sinα) and C(-10sinα, 10cosα), be the vertices of a triangle. If L(a,9) and G(h,k) be its orthocenter and centroid respectively, then (5
145
Let a be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle α with the positive x-axis and the equations of its dia
48
Let the triangle PQR be the image of the triangle with vertices (1,3), (3,1), and (2,4) in the line x + 2y = 2. If the centroid of PQR is the point (α, β), then
22
A line passing through the point P(a, θ) makes an acute angle α with the positive x-axis. Let this line be rotated about the point P through an angle (α)/(2) in
The problem is underdetermined. The value of 3a² tan² α - 2√3 simplifies to a² - 2√3. However, the value of a cannot be uniquely determined from the given infor
Let the area of the triangle formed by a straight line L: x + by + c = 0 with coordinate axes be 48 square units. If the perpendicular drawn from the origin to
97
Find the distance of the point (3, -5) from the line 3x - 4y - 26 = 0.
The distance of the point (3, -5) from the line 3x - 4y - 26 = 0 is (3)/(5).
Find the distance between the parallel lines 3x - 4y +7 = 0 and 3x - 4y + 5 = 0.
The distance between the parallel lines is (2)/(5) units.
If the orthocentre of the triangle formed by the lines y = x + 1, y = 4x - 8 and y = m x + c is at (3, -1), then m - c is:
0
Write the equation of the line through the points (1, -1) and (3, 5).
The equation of the line is y = 3x - 4.
Let the lines 3x - 4y - α = 0, 8x - 11y - 33 = 0, and 2x - 3y + = 0 be concurrent. If the image of the point (1, 2) in the line 2x - 3y + = 0 is ((87)/(13), (-6
(1073)/(8)
Find the equation of the line through ( -2, 3) with slope -4.
The equation of the line is y = -4x - 5.
If the lines 2x + y - 3 = 0, 5x + ky - 3 = 0 and 3x - y - 2 = 0 are concurrent, find the value of k.
The value of k is -2.
Find the distance of the line 4x - y = 0 from the point P (4, 1) measured along the line making an angle of 135^° with the positive x-axis.
The distance is 3√2 units.
Find the equation of the line, which makes intercepts -3 and 2 on the x- and y-axes respectively.
The equation of the line is 2x - 3y + 6 = 0.
Write the equation of the lines for which tanθ = (1)/(2), where θ is the inclination of the line and (i) y-intercept is (-3)/(2) (ii) x-intercept is 4.
(i) y = (1)/(2)x - (3)/(2) (ii) y = (1)/(2)x - 2
Let ABC be the triangle such that the equations of lines AB and AC be 3y - x = 2 and x + y = 2, respectively, and the points B and C lie on the x-axis. If P is
6 square units
The angle between two lines is (π)/(4) and slope of one of the lines is (1)/(2) find the slope of the other line.
The slope of the other line can be either -(1)/(3) or 3.
Consider the lines x(3 +1)+y(7 +2)=17 +5, being a parameter, all passing through a point P. One of these lines (say L) is farthest from the origin. If the dista
20
Line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.
The value of x is 4.

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