Find the equation of the common tangent of parabola y2=4ax and x2=4by.
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 .