Arts (English Medium) इयत्ता ११ - CBSE Question Bank Solutions for Mathematics

A straight line passes through the point (α, β) and this point bisects the portion of the line intercepted between the axes. Show that the equation of the straight line is \[\frac{x}{2 \alpha} + \frac{y}{2 \beta} = 1\].

Find the equation of the line which passes through the point (3, 4) and is such that the portion of it intercepted between the axes is divided by the point in the ratio 2:3.

Find the equation of the straight line which passes through the point (−3, 8) and cuts off positive intercepts on the coordinate axes whose sum is 7.

Find the equation of a line which passes through the point (22, −6) and is such that the intercept of x-axis exceeds the intercept of y-axis by 5.

Find the equation of the line, which passes through P (1, −7) and meets the axes at A and Brespectively so that 4 AP − 3 BP = 0.

Find the equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

Find the equation of the straight line which passes through the point P (2, 6) and cuts the coordinate axes at the point A and B respectively so that \[\frac{AP}{BP} = \frac{2}{3}\] .

Find the equations of the straight lines each of which passes through the point (3, 2) and cuts off intercepts a and b respectively on X and Y-axes such that a − b = 2.

Find the equations of the straight lines which pass through the origin and trisect the portion of the straight line 2x + 3y = 6 which is intercepted between the axes.

Find the equation of the straight line passing through the point (2, 1) and bisecting the portion of the straight line 3x − 5y = 15 lying between the axes.

Find the equation of the straight line passing through the origin and bisecting the portion of the line ax + by + c = 0 intercepted between the coordinate axes.

A straight line drawn through the point A (2, 1) making an angle π/4 with positive x-axis intersects another line x + 2y + 1 = 0 in the point B. Find length AB.

The straight line through P (x₁, y₁) inclined at an angle θ with the x-axis meets the line ax + by + c = 0 in Q. Find the length of PQ.

A line is such that its segment between the straight lines 5x − y − 4 = 0 and 3x + 4y − 4 = 0 is bisected at the point (1, 5). Obtain its equation.

Find the equation of straight line passing through (−2, −7) and having an intercept of length 3 between the straight lines 4x + 3y = 12 and 4x + 3y = 3.

Find the equation of the line passing through the point of intersection of the lines 4x − 7y − 3 = 0 and 2x − 3y + 1 = 0 that has equal intercepts on the axes.

If the straight line \[\frac{x}{a} + \frac{y}{b} = 1\] passes through the point of intersection of the lines x + y = 3 and 2x − 3y = 1 and is parallel to x − y − 6 = 0, find a and b.

Three sides AB, BC and CA of a triangle ABC are 5x − 3y + 2 = 0, x − 3y − 2 = 0 and x + y − 6 = 0 respectively. Find the equation of the altitude through the vertex A.

Find the equation of the line passing through the intersection of the lines 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.

Find the equation of the straight line passing through the point of intersection of the lines 5x − 6y − 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x − 5y + 11 = 0 .