## Question

### Solution

#### SIMILAR QUESTIONS

If *p*, *x*_{1}, *x*_{2}*….x _{i}*,….and

*q y*

_{1},

*y*

_{2},…

*y*… are in A.P. with common difference

_{i }*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 *x*^{3} – 3*px*^{3} + 3*qx *– 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 *px*^{2} + *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 locus of a point which moves such that its distance from the point (0, 0) is twice its distance from the *y *– axis.