If The Axes Are Turned Through 450. Find The Transformed From The Equation                           3x2 + 3y2 + 2xy = 2

O(0, 0), P(–2, –2) and Q(1, –2) are the vertices of a triangle, R is a point on PQ such that PR : RQ 

If three vertices of a rectangular are (0, 0), (a, 0) and (0, b), length of each diagonal is 5 and the perimeter 14, then the area of the rectangle is

If the line joining the points A(a², 1) and B(b², 1) is divides in the ratio b : a at the pint P whose x-coordinate is 7, their

If two vertices of a triangle are (3, –5) and (–7, 8) and centroid lies at the pint (–1, 1), third vertex of the triangle is at the point (a, b) then

α is root of the equation x² – 5x + 6 = 0 and β is a root of the equation x²– x – 30 = 0, then coordinates  of the point P farthest from the origin are

 are two points whose mid-point is at the origin.  is a point on the plane whose distance from the origin is

Locus of the point P(2t² + 2, 4t + 3), where t is a variable is

If the coordinates of A_n are (n, n²) and the ordinate of the center of mean position of the points A₁, A₂, … A_n is 46, then n is equal to

Area of the triangle with vertices A(3, 7), B(–5, 2) and C(2, 5) is denoted by Δ. If Δ_A, Δ_B, Δ_C denote the areas of the triangle with vertices OBC, AOC and ABO respectively, O being the origin, then

                 A₁, A₂, A₃, …. An are n points in a plane whose coordinates are (x₁, y₁), (x₂, y₂), (x₃, y₃) …, (x_n, y_n) respectively

A₁, A₂ is dissected at the point G₁, G₁ A₃ is divided in the ratio  1 : 2 at G₂, G₂ A₄ is divided in the ratio 1 : 4 at G₄, and so on until all n points are exhausted. The coordinates of the final point G so obtained are