If O is The Origin And The Coordinates Of A and B are (51, 65) And (75, 81) Respectively. Then  is Equal To

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

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

                          3x² + 3y² + 2xy = 2

                 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

If x₁ = a, y₁ = b; x₁, x­₂ …. x_n and y₁, y₂ …. y_n from an ascending arithmetic progressing with common difference 2 abd 4 respectively, then the coordinates of G are

Let the sides of a triangle ABC are all integers with A as the origin. If (2, –1) and (3, 6) are points on the line AB and AC respectively (lines AB andAC may be extended to contain these points), and length of any two sides are primes that differ by 50. If a is least possible lengths of the third side and S is the least possible perimeter of the triangle then aS is equal to

Vertices of a triangle are (0, 0), (41a, 37) and (–37, 41b) where a and bare the roots of the equation. 3x² – 16x + 15 = 0. The area of the triangle is equal to