Condition for which `y^2 = 4ax` and `x^2 = 4by` have common tangent

The condition that the parabolas y^2=4c(x-d) and y^2=4ax have a common normal other than X-axis (agt0,cgt0) is

If the parabolas y^2 = 4b (x - c) " and " y^2 = 8ax have a common tangent, then which one of the following is a valid choice for the ordered triad (a, b, c)?

Obtained the condition that the parabola y^(2)=4b(x-c)andy^(2)=4ax have a common normal other than x-axis (agtbgt0) .

The range of values of lambda for which the circles x^(2)+y^(2)=4 and x^(2)+y^(2)-4lambda x + 9 = 0 have two common tangents, is

The area of triangle formed by the common tangent to y^(2)=4x and x^(2)=4y and the co- ordinate axes is

Circle is drawn with end points of latus rectum of the parabola y^2 = 4ax as diameter, then equation of the common tangent to this circle & the parabola y^2 = 4ax is :

The equation of the common tangent to the parabolas y^(2)=4ax and x^(2)=4by is given by

The values of 'm' for which a line with slope m is common tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and parabola y^(2)=4ax can lie in interval:

The parabola y^(2)=4x and the circle (x-6)^(2)+y^(2)=r^(2) will have no common tangent if r is equal to