A straight line is normal to both the parabolas y2=x and x2=y. The distance of the origin from it is

A straight line is normal to both the parabolas $y^{2} = x and x^{2} = y .$ The distance of the origin from it is

A
$\frac{3}{4 \sqrt{2}}$
B
$\frac{1}{2 \sqrt{2}}$
C
$\frac{1}{\sqrt{2}}$
D
$\frac{1}{3 \sqrt{2}}$

Solution:

The equation of the common normal to $y^{2} = 4 a x and x^{2} = 4 a y is x + y = 3 a$

Here , $a = \frac{1}{4}$ . Its equation is $x + y = \frac{3}{4}$

The distance of (0, 0) from it is $\frac{3}{4 \sqrt{2}}$

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