The Number Of Points (p, Q) Such That p, Q Ïµ {1, 2, 3, 4} And The Equation px2 + qx + 1 = 0 Has Real Roots Is

If A(1, a), B(a, a²), C(a², a²) are the vertices of a triangle which are equidistance from the origin, then the centroid of the triangle ABC is at the point

Given the point A(0, 4) and B(0, –4), the equation of the locus of the pointp(x, y) such that |AP – BP| = 6 is

Coordinate (x, y) of a point P satisfy the relation 3x + 4y = 9, y = mx + 1. The number of integral value of m for which the x-coordinate of p is also an integer is

The point A(2, 3), B(3, 5), C(7, 7) and D(4, 5) are such that 

Q, R and S are the points on the line joining the points P(a, x) and T(b, y) such that PQ = QR = RS = ST.

The line joining A(bcos α, bsin α) and B(acos β, asin β) is produced to point M(x, y) so that AM : MB = b : a, then 

OPQR is square and M, N are the middle points of the sides PQ and QRrespectively then the ratio of the areas of the square and the triangle OMNis

If p, x₁, x₂….x_i,….and q y₁, y₂,…y_i … are in A.P. with common difference a and b respectively, then locus of the center of mean position of the point A_i (x_i, y_i), i = 1, 2 …n is

If α, β, γ are the real roots of the equation x³ – 3px³ + 3qx – 1 = 0, then the centroid of the triangle with vertices 

If G is the centroid and I the incentre of the triangle with vertices A(–36, 7), B(20, 7) and C(0, –8), then GI is equal to