The cartesian co-ordinates of the point on the parabola $y^{2}=x$ whose parameter is $\frac{-4}{3}$ are

The cartesian co-ordinates of the point on the parabola $y^{2}=x$ whose parameter is $\frac{-4}{3}$ are
  1. $\left(\frac{4}{9}, \frac{4}{3}\right)$
  2. $\left(\frac{4}{3}, \frac{-4}{3}\right)$
  3. $\left(\frac{4}{3}, \frac{4}{9}\right)$
  4. $\left(\frac{4}{9}, \frac{-2}{3}\right)$

Solution

$y^{2}=x \quad t=-4 / 3$ $a=\frac{1}{4}$ $\left(a t^{2}, 2 a t\right)$ $=\left(\frac{1}{4} \cdot \frac{16}{9} 4, \frac{-2}{3}\right)=\left(\frac{4}{9}, \frac{-2}{3}\right)$

Asked in: MHT CET 2020 (16 Oct Shift 1)

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