Straight Lines questions
982 published questions with worked solutions.
- Consider the following statements : 1. For an equation of a line, x +y =p, in normal form, the length of the perpendicular from...
- The points (1, 3) and (5, 1) are two opposite vertices of a rectangle. The other two vertices lie on the line y=2x+c. What is the...
- If the lines 3y+4x=1, y=x+5 and 5y+bx=3 are concurrent, then what is the value of b?
- What is the equation of the straight line which is perpendicular to y=x and passes through (3, 2)?
- The straight lines x+y-4=0, 3x+y-4=0 and x+3y-4=0 form a triangle, which is
- Let S denote the locus of the point of intersection of the pair of lines 4x - 3y = 12 , 4 x + 3 y = 12, where α varies over the...
- The straight lines l_1 and l_2 pass through the origin and trisect the line segment of the line L : 9x + 5y = 45 between the...
- Let A(0, 1), B(1, 1) and C(1, 0) be the mid-points of the sides of a triangle with incentre at the point D. If the focus of the...
- Let C( , ) be the circumcentre of the triangle formed by the lines 4x + 3y = 69, 4y – 3x = 17, and x + 7y = 61. Then ( - )^2+ +...
- Let A be the point (1, 2) and B be any point on the curve x^2+y^2=16. If the centre of the locus of the point P, which divides...
- If the line l_1: 3y – 2x = 3 is the angular bisector of the lines l_2: x – y + 1 = 0 and l_3: + + 17 = 0, then ^2+ ^2- - is equal...
- Let ( , ) be the centroid of the triangle formed by the lines 15x – y = 82, 6x – 5y = –4 and 9x + 4y = 17. Then +2 and 2 - are...
- The equations of the sides AB and AC of a triangle ABC are ( + 1)x + = 4 and + (1 – )y = + 3 respectively. Its vertex A is on the...
- The equations of the sides AB, BC and CA of a triangle ABC are : 2x + y = 0, x + py = 21a, (a 0) and x – y = 3 respectively. Let...
- A light ray emits from the origin making an angle 30° with the positive x-axis. After getting reflected by the line x + y = 1, if...
- Let P(a_1, b_1) and Q(a_2, b_2) be two distinct points on a circle with center C( 2, 3). Let O be the origin and OC be...
- For all z C on the curve C_1: |z| = 4, let the locus of the point z+ 1 z be the curve C_2. Then :
- Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles...
- Lines L_1 : y − x = 0 and L_2 : 2x + y = 0 intersect the line L_3 : y + 2 = 0 at P and Q, respectively. The bisector of the acute...
- Consider three points P = (- ( - ), - ), Q = ( ( - ), ) and R = ( ( - + ), ( - )), where 0 < , , < 4 . Then,
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