[[sin theta]x+[-cos theta]y=0],[[cot theta]x+y=0]

Solve the following systems of homogenous equations: {:(x cos theta - y sin theta = 0),(x sin theta + y cos theta = 0):}

If x cos theta + y sin theta =2 and x cos theta - y sin theta =0 , then which one of the following is true ?

The equation of the locus of the point of intersection of the straight lines x sin theta + (1- cos theta) y = a sin theta and x sin theta -(1+ cos theta) y + a sin theta =0 is:

The locus of the point of intersection of the lines x sin theta+(1-cos theta)y=a sin theta and x sin theta -(1+cos theta )y+a sin theta =0 is

If the angle 2 theta is acute, then the acute angle between the pair of lines x^(2)(cos theta-sin theta)+2 x y cos theta+y^(2)(cos theta+sin theta)=0 is

if xsin^3theta+ycos^3theta =sin theta cos theta and x sin theta -y cos theta =0 prove that x^2+y^2=1