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The equation of a common tangent to the parabolas $\mathrm{y=x^{2}}$ and $\mathrm{y=-(x-2)^{2}}$ is
Option: 1
$\mathrm{y=4(x-2)}$

Option: 2
$\mathrm{y=4(x-1)}$

Option: 3
$\mathrm{y=4(x+1)}$

Option: 4
$\mathrm{y=4(x+2)}$

Answers (1)

best_answer

$\mathrm{y=x^{2} \Rightarrow a=\frac{1}{4}}$

Let tangent to it be

And let tangent to $\mathrm{y=-(x-2)^{2}}$

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

$\mathrm{\Rightarrow y=m x+2 m+\frac{1}{4} m^{2}}$

For commo tangent

$\mathrm{-\frac{1}{4} m^{2}=-2 m+\frac{1}{4} m^{2}} \\$

$\mathrm{\Rightarrow m=0,4}$

For $\mathrm{ m=4}$ equation of common tangent is $\mathrm{ y=4 x-4}$

$\mathrm{ \Rightarrow y=4(x-1)}$

Hence correct option is 2

Posted by

Shailly goel

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