Commerce (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

Find the equation of the line passing through (0, 0) with slope m.

Find the equation of the line passing through \[(2, 2\sqrt{3})\] and inclined with x-axis at an angle of 75°.

Find the equation of the straight line which passes through the point (1,2) and makes such an angle with the positive direction of x-axis whose sine is \[\frac{3}{5}\].

Find the equation of the straight line passing through (3, −2) and making an angle of 60° with the positive direction of y-axis.

Find the equation of the straight line which divides the join of the points (2, 3) and (−5, 8) in the ratio 3 : 4 and is also perpendicular to it.

Prove that the perpendicular drawn from the point (4, 1) on the join of (2, −1) and (6, 5) divides it in the ratio 5 : 8.

Find the equations to the altitudes of the triangle whose angular points are A (2, −2), B (1, 1) and C (−1, 0).

Find the equation of the line passing through the point (−3, 5) and perpendicular to the line joining (2, 5) and (−3, 6).

Find the equation of the straight lines passing through the following pair of point :

(0, 0) and (2, −2)

Find the equation of the straight lines passing through the following pair of point:

(a, b) and (a + c sin α, b + c cos α)

Find the equation of the straight lines passing through the following pair of point :

(0, −a) and (b, 0)

Find the equation of the straight lines passing through the following pair of point :

(a, b) and (a + b, a − b)

Find the equation of the straight lines passing through the following pair of point :

(at₁, a/t₁) and (at₂, a/t₂)

Find the equation of the straight lines passing through the following pair of point :

(a cos α, a sin α) and (a cos β, a sin β)

Find the equations of the sides of the triangles the coordinates of whose angular point is  respectively  (0, 1), (2, 0) and (−1, −2).

Find the equations of the medians of a triangle, the coordinates of whose vertices are (−1, 6), (−3, −9) and (5, −8).

Find the equations to the diagonals of the rectangle the equations of whose sides are x = a, x = a', y= b and y = b'.

By using the concept of equation of a line, prove that the three points (−2, −2), (8, 2) and (3, 0) are collinear.

Find the equation to the straight line which bisects the distance between the points (a, b), (a', b') and also bisects the distance between the points (−a, b) and (a', −b').

In what ratio is the line joining the points (2, 3) and (4, −5) divided by the line passing through the points (6, 8) and (−3, −2).