Question

The equation of common tangent to the parabolas $y^2=4x$ and $x^2=4y$ is

• A. $x-y+1=0$
• B. $x+y-1=0$
• C. $x+y+1=0$
• D. $x-y-1=0$

Answer 1

The correct option is C $x+y+1=0$

Equation of any tangent to $y^2=4x$:
$y=mx+\frac{1}{m}$
Equation of tangent to $x^2=4y$:
$y=mx-m^2$
They represent same tangents, so
$\frac{1}{m}=-m^2$
$\Rightarrow m=-1$
Equation of tangent;
$y=-x-1$
$\Rightarrow x+y+1=0$