" 5.Find the envelope of the family of straight lines "y cos alpha-x sin alpha=a cos2 alpha

Find the intercepts on the axes made by the straight lines : x cos alpha+y sin alpha=sin2 alpha .

Find the locus of the point of intersection of lines x cos alpha+y sin alpha=a and x sin alpha-y cos alpha=b(alpha is a variable )

Find the value of sin^6 alpha+ cos^6 alpha+ 2sin^2 alpha cos^2 alpha .

Find the value of p so that the straight line x cos alpha + y sin alpha - p may touch the circle x^(2) + y^(2)-2ax cos alpha - 2ay sin alpha = 0 .

Condition when variable is involved : (ii) Find the locus of point of intersection of the lines x cos alpha+y sin alpha=a and x sin alpha-y cos alpha=b where b is the variable.

Prove that the area of the parallelogram formed by the lines x cos alpha+y sin alpha=p,x cos alpha+y sin alpha=q,x cos beta+y sin beta=r and x cos beta+y sin beta=sis+-(p-q)(r-s)csc(alpha-beta)

Find the area of the triangle formed by the straight line x sin alpha + y cos alpha = p with the axes of coordinates .

Show that the equation of a line passing through the point (a cos^(3)alpha,a sin^(3)alpha) and perpendicular to the line x sec alpha+y cos ec alpha=a is x cos alpha-sin alpha=a cos2 alpha

Locus of the point of intersection of the lines x cos alpha+y sin alpha=a and x sin alpha-y cos alpha=b where alpha is variable.

The locus of the point of intersection of the lines x cos alpha+y sin alpha =a and x sin alpha-y cos alpha=b , where alpha is a parameter is