Axes Are Rotating Through a +ive Obtuse Angle θ So That The Transformed Equation Of The Curve 3x2 – 6xy + 3y2 + 7x – 3 = 0 Is Free From The Term Of xy then The Coefficient Of x2 in The Transformed Equation Is…

A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 is

Let P = (–1, 0), Q = (0, 0) and  be three points. Then the equation of the bisector of the angle PQR is

Area of Δ formed by line x + y = 3 and  bisectors of pair of straight lines x² – y² +2y = 1is

The equation of the straight line which passes through the point (1, –2) and cuts off equal intercepts from the axes will be

The three lines 3x + 4y + 6 = 0,  and 4x + 7y + 8 = 0 are

The line (p + 2q)x + (p – 3q)y = p – q for different values of p and qpasses through the point

The locus of the mid-point of te portion intercepted between the axes by the line  where p is constant is

The straight line passing through the point of intersection of the straight lines x – 3y + 1 = 0 and 2x + 5y – 9 = 0 and having infinite slope and at a distance 2 unit from the origin has the equation

shifting of origin (0, 0) to (h, k)

                  Rotation of axes through an angle θ.

1:- by rotating the axes through an angle θ the equation xy – y² – 3y + 4 = 0 is transformed to the from which does not contain the term of xy then  ….

 A₁(x₁, y₁), A₂(x₂, y₂), A₃(x₃, y₃), …. are n points in a plane such that

1:- A₁ A₂ is at G₁, G₂, A₃ is divided in the ratio 1 : 2 at G₂, G₃, A₄ is divided in the ratio 1 : 3 at G₃. The process is continued unit all n points are exhausted, then find the coordinates of the final point G_n