If the tangent to the parabola $y^2 = x$ at a point $\left( {\alpha ,\beta } \right)\,,\,\left( {\beta > 0} \right)$ is also a tangent to the ellipse, $x^2 + 2y^2 = 1$, then $a$ is equal to
If the tangent to the parabola $y^2 = x$ at a point $\left( {\alpha ,\beta } \right)\,,\,\left( {\beta > 0} \right)$ is also a tangent to the ellipse, $x^2 + 2y^2 = 1$, then $a$ is equal to
- [JEE MAIN 2019]
- A
$2\sqrt 2 + 1$
- B
$\sqrt 2 - 1$
- C
$\sqrt 2 + 1$
- D
$2\sqrt 2 - 1$
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