Question

The equation of the common tangents to the parabola $y=x^2$ and $y=-(x-2{)}^2$ is/are

• A. $y=4(x-1)$
• B. $x=0$
• C. $y=-4(x-1)$
• D. $y=30x-50$

Answer 1

The correct option is A $y=4(x-1)$

Equation of tangent to $x^2=y$ is
$y=mx-\frac{1}{4}{m}^2$ ... (1)
Equation of tangent to $(x-2{)}^2=-y$ is
$y=m(x-2)+\frac{1}{4}{m}^2$ ... (2)
(1) and (2) are identical.
$\Rightarrow m=0$ or 4
$\Rightarrow$ Common tangents are $y=0$ and $y=4x-4$.