If `p` and `q` are the lengths of the perpendiculars from the origin to the straight lines `x sec alpha+y cosec alpha=a` and `x cos alpha-y sin alpha=a cos 2alpha, ` prove that `4p^(2)+q^(2)=a^(2)`

If p and p' are the distances of the origin from the lines x "sec" alpha + y " cosec" alpha = k " and " x "cos" alpha-y " sin" alpha = k "cos" 2alpha, " then prove that 4p^(2) + p'^(2) = k^(2).

If p and q are respectively the perpendiculars from the origin upon the striaght lines, whose equations are x sec theta + y cosec theta =a and x cos theta -y sin theta = a cos 2 theta , then 4p^(2) + q^(2) is equal to

Find the length of perpendicular from the point (a cos alpha, a sin alpha) to the line x cos alpha+y sin alpha=p .

Locus of the point of intersection of lines x cosalpha + y sin alpha = a and x sin alpha - y cos alpha =b (alpha in R ) is

If p sin^(3)alpha+qcos^(3)alpha=sinalphacosalpha and p sinalpha - q cos alpha=0, then prove that : p^(2)+q^(2)=1

Simplify be reducing to a single term : sin 3 alpha cos 2 alpha + cos 3 alpha sin 2 alpha.

If the line y cos alpha = x sin alpha +a cos alpha be a tangent to the circle x^(2)+y^(2)=a^(2) , then

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 .

The coordinates of the point at which the line x cos alpha + y sin alpha + a sin alpha = 0 touches the parabola y^(2) = 4x are

Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + cos 2(alpha + beta) = cos 2alpha