Question

The equation of the common tangent to the parabolas y² = 32x and x² = 108y is

• A. $2x + 3y + 36 = 0$
• B. $3x + 2y + 108 = 0$
• C. $3x + 2y - 36 = 0$
• D. $2x + 3y - 108 = 0$

Answer 1

Answer: (A)

$2x + 3y + 36 = 0$

Answer 2

The equation of the common tangent to two parabolas

y² = 4ax and x² = 4by is$a^{1/3}x + b^{1/3}y + a^{2/3}b^{2/3} = 0$.

∴ The common tangent to the given parabolas is

2x+3y+36 = 0.