Find The Locus Of A Point Which Moves Such That Its Distance From The Point (0, 0) Is Twice Its Distance From The y – Axis.

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

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 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

Consider the point   then

A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is

Find the co – ordinates of the point which divides the line segment joining the pints (5, – 2) and (9, 6) in the ratio 3 : 1.

Find the co – ordinates of a point which divides externally the line joining (1, –3) and (–3, 9) in the ratio 1 : 3.

Two vertices of a triangle are (–1, 4) and (5, 2). If its centroid is (0, –3), find the third vertex.

Find the area of the pentagon whose vertices are A(1, 1), B(7, 21), C(7, –3), D(12, 2) and (0, –3).

Find the equation of the curve 2x² + y² – 3x + 5y – 8 = 0 when the origin is transferred to the point (–1, 2) without changing the direction of axes.