The centre of the circle passing through the point $(0,1)$ and touching the parabola $y=x^{2}$ at the point $(2,4)$ is
The centre of the circle passing through the point $(0,1)$ and touching the parabola $y=x^{2}$ at the point $(2,4)$ is
- [JEE MAIN 2020]
- A
$\left(\frac{3}{10}, \frac{16}{5}\right)$
- B
$\left(\frac{-16}{5}, \frac{53}{10}\right)$
- C
$\left(\frac{6}{5}, \frac{53}{10}\right)$
- D
$\left(\frac{-53}{10}, \frac{16}{5}\right)$
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