Question

The common tangent to the parabola $y^2=32x$ and $x^2=256y$ will be_________

• A. $2x+4y+64=0$
• B. $x+2y-32=0$
• C. $2x+4y+32=0$
• D. $4xx+2y+64=0$

Answer 1

Answer: (A)

Given parabolas are,
$y^2=32x$ and $x^2=256y$
We use a standard result to find equation of common tangent.
Equation of tangent common to $y^2=4ax$ and $x^2=4by$ is,
$b^{1/3}y+a^{1/3}x+{\left(a^2{b}^2\right)}^{1/3}=0$
Here, $4a=32\Rightarrow a=8$
$4b=256,b=64$
So tangent is,
$(64{)}^{1/3}y+(8{)}^{1/3}x+{\left(8^2\times 64^2\right)}^{1/3}=0$
$\Rightarrow 4y+2x+64=0$