Let `L_1` be a tangent to the parabola `y^(2) = 4(x+1) and L_2` be a tangent to the parabola `y^(2) = 8(x+2)` such that `L_1 and L_2` intersect at right angles. Then `L_1 and L_2` meet on the straight line :

Let a line L : 2x + y = k, k gt 0 be a tangent to the hyperbola x^(2) - y^(2) = 3 . If L is also a tangent to the parabola y^(2) = alpha x , then alpha is equal to

Let L be a tangent line to the parabola y^(2)=4x - 20 at (6, 2). If L is also a tangent to the ellipse (x^(2))/(2)+(y^(2))/(b)=1 , then the value of b is equal to :

A tangent line L is drawn at the point (2, -4) on the parabola y^(2) = 8x . If the line L is also tangent to the circle x^(2) + y^(2) = a , then 'a' is equal to ________.

Consider the following lines : L_(1) : x-y-1=0 L_(2):x+y-5=0 L_(3):y-4=0 Let L_(1) is axis to a parabola, L_(2) is tangent at the vertex to this parabola and L_(3) is another tangent to this parabola at some point P. Let 'C' be the circle circumscribing the triangle formed by tangent and normal at point P and axis of parabola. The tangent and normals at normals at the extremities of latus rectum of this parabola forms a quadrilateral ABCD. Q. The equation of the circle 'C' is :