Question

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

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

Answer 1

Answer: (A), (B)

The correct options are
A $y=4(x-1)$
B $y=0$

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 $y=4x-4$.