If the line `ax+ by =1` passes through the point of intersection of `y =x tan alpha + p sec alpha, y sin(30^@-alpha)-x cos (30^@-alpha) =p`, and is inclined at `30^@` with `y=tan alpha x` , then prove that `a^2 + b^2 = 3/(4p^2)` .

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

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 )

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 intersection point of x cos alpha+y sin alpha=a and x sin alpha-y cos alpha=b is

The locus of the point of intersection of the lines x cosalpha + y sin alpha= p and x sinalpha-y cos alpha= q , alpha is a variable will be

(x tan alpha+y cot alpha)(x cot alpha+y tan alpha)-4xy cos^(2)2 alpha=

If the point (3, 4) lies on 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 ( alpha is a variable), the point (a, b) lies on the line 3x-4y=0 then (a^(2)-b^(2))/2 is equal to

tan^(2)alpha=1-p^(2) then sec alpha+tan^(3)alpha*cos ec alpha

If the point (3,4) lies on 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 ( alpha is a variable) ,the point (a, b) lies on the line 3x-4y=0 then |a+b| is equal to