A variable line through the point `((6)/(5),(6)/(5))` cuts the coordinate axes at the points A and B respectively. If the point P divides AB internally in the ratio `2:1`, then the equation of the locus of P is

A variable line through the point (6/5, 6/5) cuts the coordinates axes in the point A and B . If the point P divides AB internally in the ratio 2:1 , show that the equation to the locus of P is :

Find the equation of straight line which passes through the point P(2,6) and cuts the coordinate axis at the point A and B respectively so that AP:BP=2:3.

A (2, 3) is a fixed point and Q(3 cos theta, 2 sin theta) a variable point. If P divides AQ internally in the ratio 3:1, find the locus of P.

The coordinates of the point A and B are (a,0) and (-a ,0), respectively. If a point P moves so that P A^2-P B^2=2k^2, when k is constant, then find the equation to the locus of the point P .

The coordinates of the point A and B are (a,0) and (-a ,0), respectively. If a point P moves so that P A^2-P B^2=2k^2, when k is constant, then find the equation to the locus of the point Pdot

A straight line passes through the points P(-1, 4) and Q(5,-2). It intersects the co-ordinate axes at points A and B. M is the midpoint of the segment AB. Find : The equation of the line.

A straight line through the origin 'O' meets the parallel lines 4x +2y= 9 and 2x +y=-6 at points P and Q respectively. Then the point 'O' divides the segment PQ in the ratio

A variable plane at a constant distance p from the origin meets the coordinate axes in points A,B and C respectively.Through these points , planes are drawn parallel to the coordinate planes, show that locus of the point of intersection is 1/x^2+1/y^2+1/z^2=1/p^2

A straight line passes through the points A(-5, 2) and B(3,-6). It intersects the co-ordinate axes at points C and D . Find : the equation of AB.

A straight line passes through the points A(-5, 2) and B(3,6). It intersects the co-ordinate axes at points C and D . M is a point on AB which divides CD in the ratio 1: 2. Find : the co-ordinates of points C and D.