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

Find the condition that the line x cos alpha+y sin alpha=p touches the parabola y^(2)=4ax

The angle between the lines x cos alpha + y sin alpha = a and x sin beta - y cos alpha = a is

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

Prove that the locus of the points of intersection of the lines x cos alpha + y sin alpha = a and x sin alpha - y cos albha = b is a cicle, whatever may be 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

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

Show that the locus of the point of intersection of the lines x cos alpha + y sin alpha = a and x sin alpha - y cos alpha = a , when alpha varies, is a circle.

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