If A = (3, 4) and B is a variable point on the lines |x| = 6 If `AB le 4` then the number of positions of B with integral co-ordinates is :

Consider the point A(3,4) and B(7,13).If P be a point on the line y=x, the co-ordinate of point P if PA+PB is minimum.

Find the cartesian co-ordinates of the points whose polar co-ordinates are (3,pi/6)

Find the cartesian co-ordinates of the points whose polar co-ordinates are (5,pi/4)

The line joing two points A(2,0)and B(3,1)I rotated about A in anti clockwise direction through an angle of 15^@ .If B goes to C in the new position,what will be the co-ordinates of C?

If the straight line (x)/(a) + (y)/(b) = 1 is parallel to the line 4x + 3y = 6 and passes through the point of intersection of the lines 2x - y - 1 = 0 and 3x - 4y + 6 = 0 ,find the values of a and b .

Let AB be a line segment of length 4 unit with the point A on the line y=2x and B on the line y=x. Then locus of middle point of all such line segment is

The number of lines that are parallel to 2x + 6y -7 = 0 and have an intercept 10 between the co-ordinates axis is :

A(2,5) and B(-3,-4) are two fixed points , the point P divides the line -segment overline(AB) internally in the ratio k:1 . Find the coordinates of P . Hence find the equation of the line joining A and B.

Consider the point A(3,4)and B(7,13).If be a point on the line y=x,such that |PA+PB| is minimum, then co-ordinate of P is

If vec(a)=4vec(i)-3hat(j) " and " vec(b)=-2hat(i)+5hat(j) are the position vectors of the points A and B respectively, find (i) the position vector of the middle point of the line-segment bar(AB) , (ii) the position vectors of the points of trisection of the line-segment bar(AB) .