Question

The equation of common tangent of the parabolas

Answer 1

Let the equation of common tangent to y2 = 4ax and x2 = 4 by be y = mx + c.

y = mx + c is the tangent to the parabola y2 = 4ax.


is tangent to the parabola x2 = 4 by, then it will cut the parabola x2 = 4 by in two coincidental points.



mx2 = 4bm2x + 4ab

mx2 – 4bm2x – 4ab = 0

∴ D = (– 4bm2)2 – 4 × m × (– 4ab) = 0


Equation of the common tangent is



Thus, the equation of the common tangent is