Question

The common tangent to the parabolas $y^2=4ax$ and $x^2=32ay$ has the equation

• A. $x-2y-4a=0$
• B. $x+2y+4a=0$
• C. $x+2y-4a=0$
• D. $x-2y+4a=0$

Answer 1

The correct option is B $x+2y+4a=0$

For common tangent, the slope of tangent to $y^2=4ax$ must be equal to the slope of tangent to $x^2=32ay$.
$\Rightarrow \frac{a}{m}=-\left(8a\right)m^2$.
$\therefore m=-\frac{1}{2}$
$\therefore$ Equation of common tangent is $y=mx+\frac{a}{m}$
Substituting values, we get,
$y=\frac{-x}{2}-2a$
or $x+2y+4a=0$