Given that A♢B=4A−B, what is the value of (3♢2)♢3?
If the lines joining the origin and the point of intersection of curves ax2+2hxy+by2+2gx+0 and a1x2+2h1xy+b1y2+2g1x=0 are mutually perpendicular, then prove that g(a1+b1)=g1(a+b)˙
If one of the lines denoted by the line pair ax2+2hxy+by2=0 bisects the angle between the coordinate axes, then prove that (a+b)2=4h2
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
Find the equation of the lines through the point (3, 2) which make an angle of 45owith the line x−2y=3.
Find the equation of a line drawn perpendicular to the line 4x+6y=1through the point, where it meets the yaxis
If x2+2hxy+y2=0 represents the equation of the straight lines through the origin which make an angle α with the straight line y+x=0 (a)sec2α=h cosα (b)=(2h)(1+h) (c)2sinα =h(1+h) (d) cotα =(h−1)(1+h)
Find the equation of the line which satisfy the given conditions : Passing through the point (−1,1)and (2,−4)