A Straight Line Passes Through (2, 3) And The Portion Of The Line Intercepted Between The Axes Is Bisected At This Point. Find Its Equation

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

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

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

Find the area of triangle ABC with vertices A (a, a²), B (b, b²), C (c, c²).

Find the slope (m), intercepts on X axis, intercept on Y axis of the line 3x+ 2y – 12 = 0. Also trace the line on XY plane.