Straight Lines questions
982 published questions with worked solutions.
- If the pair of lines ax^2+2hxy+by^2+2gx+2fy+c=0 intersect on the y-axis then
- The combined equation of three sides of a triangle is (x^2-y^2)(2x+3y-6)=0. If (-2,a) is an interior point and (b,1) is an...
- Three sides of a triangle have the equations L_r y - m_r x - c_r = 0; r = 1, 2, 3. Then L_2L_3 + L_3L_1 + L_1L_2 = 0, where 0, 0,...
- A ray of light incident at the point (-2,-1) gets reflected from the tangent at (0,-1) to the circle x^2+y^2=1. The reflected ray...
- The locus of the centre of a circle touching the lines x+2y=0 and x-2y=0 is
- A ray of light moving parallel to the x-axis gets reflected from a parabolic mirror whose equation is (y - 2)^2 = 4(x + 1). After...
- A vector has components 2p and 1 with respect to a rectangular cartesian system. The axes are rotated through an angle about the...
- The angle between the lines joining the points (1, 0, -3), (2, -1, 2), and (1, 1, 1), (3, 2, 0) is
- The angle between two lines whose direction cosines satisfy the equations n = l + m and m = 2l + 3n is
- The lines x+3 -2 = y 1 = z-4 3 and x = y-1 +1 = z +2 are perpendicular to each other. Then is equal to
- The angle between the lines x+2 1 = y+3 -2 = z-4 1 and x-1 -1 = y 1 = z 0 is
- If the lines x1= y2= z3, x-1 3 = y-2 -1 = z-3 4 and x+k 3 = y-1 2 = z-2 h are concurrent then
- The real value of a for which the value of m satisfying the equation (a^ 2 -1)m^ 2 -(2a-3)m+a=0 gives the slope of a line...
- The angle between the straight lines joining the point (-1, 0) to the common points of 3x^2 + 5xy - 3y^2 + 8x + 8y + 5 = 0 and 3x...
- A variable line x a + y b = 1 is drawn through the point (k, 2k) so as to form a triangle of area A. If a, b are of the same sign...
- If the coordinates of two vertices and the orthocentre of a triangle are integers then the coordinates of the third vertex must be
- Let PQR be a right-angled triangle, right angled at P(2, 1). If the equation of the line QR is 2x + y = 3 and Q = (2, -1) then...
- If in the triangle ABC the equation of the side BC is x + 2y = 3, the vertex A is (1, 2) and the abscissa of the orthocentre is 3...
- If the algebraic sum of the distances of the points (1, 2), (-3, 1) and (2, -5) from a straight line be equal to zero then the...
- Two gas companies G_1 and G_2, situated at (40,0) and (0,30) respectively (unit of distance = 1 km), offer to install equally...
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