Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :

If the line 3x + 4y – 24 = 0 intersects the x-axis at the point A and the y-axis at the point B, then the incentre of the triangle OAB, where O is the origin, is

Two vertices of a triangle are (0,2) and (4,3). If its orthocentre is at the origin, then its third vertex lies in which quadrant ?

If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the equation of the diagonal AD is:-

If a straight line passing through the point P(–3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is :

If α, β, γ are the real roots of the equation x³ – 3px² + 3qx – 1 = 0, then the centroid of the triangle whose vertices are 

Consider  the family of lines x(a + b) + y = 1, where a, b and c are the roots of the equation x³ – 3x² + x + λ = 0 such that c ∈ [1,2]. If the given family of lines makes triangle of area 'A' with coordinate axis, then maximum value of 'A' (in sq. units) will be  -

Line AB passes through point (2, 3) and intersects the positive x and y axes at A(a, 0) and B(0, b) respectively. If the area of ΔAOB is 11, the numerical value of 4b² + 9a², is :-

An insect is resting on the graph paper at a point A(3, 2). Now it starts moving towards west direction and covers a distance of 4 units and then it turns towards south and covered a distance of 3 units and reaches at point B then the polar co-ordinates of point B will be :-

The equation of the perpendicular bisectors of the sides AB and AC of a triangle ABC are y = x and y = –x, respectively. If the point A is (1, 2), then the area of ΔABC is :-