Frequent Straight Line Questions

Prove that two of the straight lines represented by equation ax^3 + bx^2y + cxy^2 + dy^3 =0 will be at right angled if a^2 + ac + bd + d^2 =0. ...

if the point [3,4] lies on the locus of the point of intersection of the lines xcos(α)+ysin(α)=a and xsin(α)-ycos(α)=b, (α is variable), the point (a,b) lies on the line 3x-4y=0 then 9a4+16b4+34 is equal to ...

two fixed pt.s A and B are taken on the axes such that OA=a and OB=b ; two variable point A1 and B1 are taken on the same axes;find the locus of intersection of A1B and B1A: 1. when OA1 + OB1=OA + OB 2. when 1/OA1 - 1/OB1 = 1 ...