A(3,0) and B(6,0) are two fixed points and U `(x_1 ,y_1)` is a variable point on the plane ,
AU and BU meet the y - axis at C and D respectively and AD meets OU at V.
Prove that CV passes through (2,0) for any position of U in the plane .

the image of the point (-1,3,4) in the plane x-2y=0

A line through the variable point A(k+1,2k) meets the lines 7x+y-16=0,5x-y-8=0,x-5y+8=0 at B ,C ,D , respectively. Prove that A C ,A B ,A D are in HP.

A horizontal plane 4x-3y+7z=0 is given. Find a line of greatest slope passes through the point (2, 1, 1) in the plane 2x+y-5z=0 .

A straight line through A (-15 -10) meets the lines x-y-1=0 , x+2y=5 and x+3y=7 respectively at A, B and C. If 12/(AB)+40/(AC)=52/(AD) prove that the line passes through the origin.

For points P -= (x_(1) ,y_(1)) and Q = (x_(2),y_(2)) of the coordinate plane , a new distance d (P,Q) is defined by d(P,Q) = |x_(1)-x_(2)|+|y_(1)-y_(2)| Let O -= (0,0) ,A -= (1,2), B -= (2,3) and C-= (4,3) are four fixed points on x-y plane Let R(x,y) such that R is equidistant from the point O and A with respect to new distance and if 0 le x lt 1 and 0 le y lt 2 , then R lie on a line segment whose equation is

Prove that the line through the point (x_1,y_1) and parallel to the line Ax + By + C = 0 is A (x- x_1) + B (y -y_1) = 0.

The circle passing through the point ( -1,0) and touching the y-axis at (0,2) also passes through the point.

A variable plane passes through a fixed point a,b,c and meet the co-ordinates axes in A,B,C. Show that the locus of the point common to the planes through A,B,C parallel to the co-ordinate planes is a/x+b/y+c/z=1

Find the equation of the line passing through the point (3,0,1) and parallel to the planes x+2y=0 and 3y-z=0.