Straight Lines and Pair of Straight Lines
Showing 50 of 303 · 303 total
- 1.If a straight line drawn through the point of intersection of the lines 4 x+3 y-1=0 and 3 …Medium
- 2.In an equilateral triangle P Q R, let the vertex P be at (3,5) and the side Q R be along t…Medium
- 3.Let the line L_1:x+3=0 intersect the lines L_2:x-y=0 and L_3:3x+y=0 at the points A and B …Hard
- 4.Let the vertex A of a triangle ABC be (1,2), and the mid-point of the side AB be (5,-1).Medium
- 5.Let the mid points of the sides of a triangle ABC be ((5)/(2),7), ((5)/(2),3) and (4,5).Medium
- 6.Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the l…Medium
- 7.Let the angles made with the positive x-axis by two straight lines drawn from the point P(…Hard
- 8.Let A(1,0),B(2,-1) and C((7)/(3),(4)/(3)) be three points.Medium
- 9.Let A(1,2) and C(-3,-6) be two diagonally opposite vertices of a rhombus, whose sides AD a…Medium
- 10.A rectangle is formed by the lines x=0, y=0, x=3 and y=4.Medium
- 11.Among the statements (S 1) : If A(5,-1) and B(-2,3) are two vertices of a triangle, whose …Medium
- 12.Let a point A lie between the parallel lines L_1 and L_2 such that its distances from L_1 …Medium
- 13.Let a be the length of a side of a square OABC with O being the origin.Medium
- 14.A line passing through the point P(a, 0) makes an acute angle with the positive x-axis.Hard
- 15.If the orthocenter of the triangle formed by the lines y = x + 1, y = 4x - 8 and y = mx + …Medium
- 16.Let ABC be the triangle such that the equations of lines AB and AC be 3 y-x=2 and x+y=2, r…Medium
- 17.Let the three sides of a triangle are on the lines 4 x-7 y+10=0, x+y=5 and 7 x+4 y=15.Medium
- 18.Consider the lines x(3 +1)+y(7 +2)=17 +5, being a parameter, all passing through a point P…Medium
- 19.A line passes through the origin and makes equal angles with the positive coordinate axes.Medium
- 20.Let the area of the triangle formed by a straight line L:x+by+c=0 with co-ordinate axes be…Medium
- 21.Let the line x + y = 1 meet the axes of x and y at A and B, respectively.Hard
- 22.Let ABC be a triangle formed by the lines 7x -- 6y + 3 = 0, x + 2y -- 31 = 0 and 9x -- 2y …Medium
- 23.Two equal sides of an isosceles triangle are along -x + 2y = 4 and x + y = 4 .Medium
- 24.If A and B are the points of intersection of the circle x^2 + y^2 - 8x = 0 and the hyperbo…Hard
- 25.Let the points ((11)/(2), ) lie on or inside the triangle with sides x+y=11,x+2y=16 and 2x…Medium
- 26.Let the lines 3x-4y- =0,8x-11y-33=0, and 2x-3y+ =0 be concurrent.Medium
- 27.A rod of length eight units moves such that its ends A and B always lie on the lines x-y+2…Hard
- 28.Let the triangle PQR be the image of the triangle with vertices (1,3),(3,1) and (2,4) in t…Medium
- 29.A variable line L passes through the point (3,5) and intersects the positive coordinate ax…Medium
- 30.A ray of light coming from the point P(1,2) gets reflected from the point Q on the x-axis …Medium
- 31.If the line segment joining the points (5,2) and (2,a) subtends an angle ( )/(4) at the or…Medium
- 32.The equations of two sides AB and AC of a triangle ABC are 4x+y=14 and 3x-2y=5, respective…Medium
- 33.If the locus of the point, whose distances from the point (2,1) and (1,3) are in the ratio…Medium
- 34.Let a variable line of slope m>0 passing through the point (4,-9) intersect the coordinate…Medium
- 35.Let A(-1,1) and B(2,3) be two points and P be a variable point above the line AB such that…Medium
- 36.Let two straight lines drawn from the origin O intersect the line 3x+4y=12 at the points P…Medium
- 37.The vertices of a triangle are A(-1,3),B(-2,2) and C(3,-1).Medium
- 38.Let A(a, b), B(3,4) and C(-6,-8) respectively denote the centroid, circumcentre and orthoc…Medium
- 39.Let , , , Z and let A( , ),B(1,0),C( , ) and D(1,2) be the vertices of a parallelogram ABC…Medium
- 40.If x^2-y^2+2 h x y+2 g x+2 f y+c=0 is the locus of a point, which moves such that it is al…Medium
- 41.A line passing through the point A(9,0) makes an angle of 30^ with the positive direction …Easy
- 42.Let A be the point of intersection of the lines 3x+2y=14,5x-y=6 and B be the point of inte…Easy
- 43.The distance of the point (2,3) from the line 2 x-3 y+28=0, measured parallel to the line …Medium
- 44.In a [ A B C], suppose y=x is the equation of the bisector of the angle B and the equation…Medium
- 45.Let R be the interior region between the lines 3x-y+1=0 and x+2y-5=0 containing the origin…Medium
- 46.The portion of the line 4 x+5 y=20 in the first quadrant is trisected by the lines L_1 and…Medium
- 47.If ( , ) is the orthocenter of the triangle ABC with vertices A(3,-7),B(-1,2) and C(4,5), …Medium
- 48.Let ( , ) be the centroid of the triangle formed by the lines 15x-y=82,6x-5y=-4 and 9x+4y=…Medium
- 49.If the point ( ,7√33) lies on the curve traced by the mid-points of the line segments of t…Medium
- 50.Let C( , ) be the circumcenter of the triangle formed by the lines 4x+3y=69 4y-3x=17, and …Medium