Distance between two parallel planes 2x+y+2z=8 and 4x+2y+4z+5=0 is
A line L passing through the point (2, 1) intersects the curve 4x2+y2−x+4y−2=0 at the point AandB . If the lines joining the origin and the points A,B are such that the coordinate axes are the bisectors between them, then find the equation of line L˙
If three lines whose equations are y=m1x+c1,y=m2x+c2and y=m3x+c3are concurrent, then show that m1(c2−c3)+m2(c3−c1)+m3(c1−c2)=0.
If one of the lines of my2+(1−m2)xy−mx2=0 is a bisector of the angle between the lines xy=0 , then m is (a)1 (b) 2 (c) −21 (d) −1
If the middle points of the sides BC,CA, and AB of triangle ABC are (1,3),(5,7), and (−5,7), respectively, then find the equation of the side AB˙
A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio 1:n. Find the equation of the line.