Area Of The Triangle With Vertices A(3, 7), B(–5, 2) And C(2, 5) Is Denoted By Δ. If ΔA, ΔB, ΔC denote The Areas Of The Triangle With Vertices OBC, AOC and ABO respectively, O being The Origin, Then

The points (a, b + c), (b, c + a) and (c, a + b) are

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

If the axes are turned through 45⁰. Find the transformed from the equation

                          3x² + 3y² + 2xy = 2