Prove that the two parabolas `y^(2) = 4ax and y^(2) = 4c (x-b)` cannot have a common normal, other than the axis, unless `(b)/(b-c) gt 2`

If the two parabolas y^2 = 4x and y^2 = (x-k) have a common normal other than x-axis, then value of k can be (A) 1 (B) 2 (C) 3 (D) 4

If the parabolas y^(2)=4ax and y^(2)=4c(x-b) have a common normal other than the x -axis (a,b,c being distinct positive real numbers),then prove that (b)/(a-c)>2

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

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 two parabolas y^(2)-4a(x-k) and x^(2)=4a(y-k) have only one common point P, then the equation of normal to y^(2)=4a(x-k) at P is

Find the angle between the parabolas y^2=4a x and x^2=4b y at their point of intersection other than the origin.

Find the area common to two parabolas x^(2)=4ay and y^(2)=4ax, using integration.

Parabolas (y-alpha)^(2)=4a(x-beta)and(y-alpha)^(2)=4a'(x-beta') will have a common normal (other than the normal passing through vertex of parabola) if

If the parabolas y=x^(2)+ax+b and y=x(c-x) touch each other at the point (1,0), then a+b+c=

If y=mx+4 is common tangent to parabolas y^(2)=4x and x^(2)=2by . Then value of b is