If The Algebraic Sum Of The Perpendicular Distances Of a variable Line From The Points (0, 2), (2, 0) And (1, 1) Is Zero, Then The Line Always Passes Through The Point

Find the distance between the lines 5x + 12y + 40 = 0 and 10x + 24y – 25 = 0.

If P is (1, 2) and the line mirror is 2x – y + 4 = 0, find the coordinates of its image (i.e., Q).

Find the values of λ for which the point (2 – λ, 1 + 2λ) lies on the non-origin side of the line 4x – y – 2 = 0. 

Find the incentre of ΔABC if A is (4, –2), B is (–2, 4) and C is (5, 5).

Find the coordinates of the orthcentre of the triangle whose vertices are (0, 0), (2, –1) and (–1, 3).

Find straight lines represented by 6x² + 13xy + 6y² + 8x + 7y + 2 = 0 and also find the point of intersection.  

If a, b, c are all distinct, then the equations (b – c)x + (c – a)y + a – b = 0 and (b³ – c³)x + (c³ – a³)y + a³ – b³ = 0 represent the same line if

If the pair of lines x² – 2pxy – y² = 0 and x² – 2qxy – y² = 0 are such that each pair bisects the angle between the other pair, then pq equals  

Angles made with x-axis by the two lines through the point  (1, 2) and cutting the line x + y = 4 at a distance  from the point (1, 2) are

 be three points. Then the equation of the bisector of angle PQR is