Straight Lines questions
982 published questions with worked solutions.
- In a ΔABC, suppose y = x is the equation of the bisector of the angle B and the equation of the side AC is 2x – y = 2. If 2AB =...
- Let (5, a/4) be the circumcentre of a triangle with vertices A(a, –2), B(a, 6) and C(a/4, –2). Let α denote the circumradius, β...
- If x² – y² + 2hxy + 2gx + 2fy + c = 0 is the locus of a point, which moves such that it is always equidistant from the lines x +...
- A line passing through the point A(9, 0) makes an angle of 30° with the positive direction of x-axis. If this line is rotated...
- Let A(−2, −1), B(1, 0), C(α, β) and D(γ, δ) be the vertices of a parallelogram ABCD. If the point C lies on 2x − y = 5 and the...
- Let the points of intersections of the lines x – y + 1 = 0, x – 2y + 3 = 0 and 2x – 5y + 11 = 0 are the mid points of the sides...
- Let A(–1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0, intersects lines AC and BC at point P and Q...
- Let k be an integer such that the triangle with vertices (k, –3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre...
- Let , and ; , , (2n-1) 2 , n N be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If...
- In a triangle PQR, the co-ordinates of the points P and Q are (–2, 4) and (4,–2) respectively. If the equation of the...
- The area of the triangle with vertices A(z), B(iz) and C(z + iz) is :
- Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be along the...
- The equation of one of the straight lines which passes through the point (1,3) and makes an angle ^ -1 ( 2) with the straight...
- A vector a has components 3p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle...
- If , are natural numbers such that 100 -99 =(100)(100)+(99)(101)+(98)(102)+ +(1)(199), then the slope of the line passing through...
- Let P be a variable point on the parabola y = 4x^2+1. Then the locus of the mid-point of the point P and the foot of the...
- For p > 0, a vector v_2 =2 i +(p+1) j is obtained by rotating the vector v_1 = 3p i + j by an angle about origin in counter...
- Consider a triangle having vertices A(–2, 3), B(1, 9) and C(3, 8). If a line L passing through the circum-centre of triangle ABC,...
- Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (–5, 0). If the locus of...
- A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes...
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