Triangle Is Formed By The Coordinates (0, 0), (0, 21) And (21, 0). Find The Numbers Of Integral Coordinates Strictly Inside The Triangle (integral Coordinates Of Both x and y)

Determiner as to what point the axes of the coordinates be shifted so as to remove the first degree terms from the equation

           f (x, y) = 2x² + 3y² – 12x + 12y + 24 = 0

What will be the coordinates of the point  when the axes are rotated through an angle of 30⁰ in clockwise sense?

What will be the coordinates of the point in original position ifr its coordinates after rotation of axes through an angle 60⁰  ?

The in centre of the triangle with vertices , (0, 0) and (2, 0) is

If a vertex of a triangle is (1, 1) and the mid-point of two sides through the vertex are (–1, 2) and (3, 2), then the centroid of the triangle is

If the equation of the locus of a point equidistant from the points

(a₁, b₁) and (a₂, b₂) is (a₁ – a₁)x + (b₁  –  b₂)y + c = 0,

Then the value of c is :

The line joining the point  is produced to the point L(x, y) so that AL : LB = b : a, then 

The vertex of a triangle are the points A(–36, 7), B(20, 7) and C(0, –8), If G and I be the centoid and in center of the triangle, then GI is equal to

If a, b, c are relation by 4a² + 9b² – 9c² + 12ab = 0 then the greatest distance between any two lines of the family of lines

ax + by + c = 0 is:

If x₁, x₂, x₃ as well as y₁, y₂, y₃ are in G.P. with the same common ratio, then the points (x₁, y₁), (x₂, y₂) and (x₃, y₃)