The equation of a common tangent to the parabolas y=x^2 and y=-(x-2)^2 is

Question

The equation of a common tangent to the parabolas $y=x^2$ and $y=-(x-2)^2$ is

Accepted Answer

Equation of tangent of slope $m$ to $y$ $= x^2$

$$y = mx - {1 \over 4}{m^2}$$

Equation of tangent of slope $m$ to $y =  - {(x - 2)^2}$

$$y = m(x - 2) + {1 \over 4}{m^2}$$

If both equation represent the same line

$${1 \over 4}{m^2} - 2m =  - {1 \over 4}{m^2}$$

$$m = 0,\,4$$

So, equation of tangent

$y = 4x - 4$

Solutions · 1