OX and OY are two coordinate axes. On OY is taken a fixed point P(0,c) and on OX any point Q. On PQ, an equilateral triangle is described, its vertex R being on the right side of PQ. Prove that the locus of R is `y =sqrt(3) x-c` .

O X and O Y are two coordinate axes. On O Y a fixed point P(0,c) is taken and on O X any point Q is taken. On P Q , an equilateral triangle is described, its vertex R being on the side of P Q away from O . Then prove that the locus of R is y=sqrt(3)x-c

Two points O(0,0) and A(3,sqrt(3)) with another point P form an equilateral triangle. Find the coordinates of Pdot

Let P be a variable point on a circle C and Q be a fixed point outside C. If R is the midpoint of the line segment PQ, then locus of R is

If one vertex of an equilateral triangle of side a, lies at the origin and the other lies on the line x-sqrt3y=0 , the coordinates of the third vertex are

The coordinates of the points A and B are (3,sqrt(3))and(0,2sqrt(3)) respectively , if ABC be an equilateral triangle find the coordinates of C.

The straight line 3x+4y-12=0 meets the coordinate axes at Aa n dB . An equilateral triangle A B C is constructed. The possible coordinates of vertex C

P is a point on the line y+2x=1, and Qa n dR two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is

The straight line through a fixed point (2,3) intersects the coordinate axes at distinct point P and Q. If O is the origin and the rectangle OPRQ is completed then the locus of R is

On the line segment joining (1, 0) and (3, 0) , an equilateral triangle is drawn having its vertex in the fourth quadrant. Then the radical center of the circles described on its sides. (a) (3,-1/(sqrt(3))) (b) (3,-sqrt(3)) (c) (2,-1/sqrt(3)) (d) (2,-sqrt(3))

Let O be the vertex and Q be any point on the parabola x^(2) = 8 y . If the point P divides the line segments OQ internally in the ratio 1 : 3 , then the locus of P is _