Question

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

• A. $x+y+a=0$
• B. $x+y=a$
• C. $x-y=a$
• D. none of these

Answer 1

The correct option is A $x+y+a=0$

Equation of tangent for parabola $y^2=4ax$ is $y=mx+\frac{a}{m}$
Equation of tangent for $x^2=4ay$ is $y=mx-a{m}^2$
Therefore for common tangent $-a{m}^2=\frac{a}{m}$
Hence $m=-1$
Equation of tangent will be $y=-x-a$

$y+x+a=0$