If the point on `y = xtanalpha -(ax^2)/(32cos^2alpha),(alpha > 0)` where the tangent is parallel to `y = x` has an ordinate `4/a` then `4sin^2alpha` equals to:

points on the curve y=4 alpha[x+alpha sin((x)/(alpha))] where the tangent is parallel to the X axis lie on

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

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

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

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

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

If the product of the intercepts make by the straight line xtan alpha+y sec alpha=1, (0 le alpha lt (pi)/2) , on the co-ordinates axes is equal to sin alpha, find alpha .