Question

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

Answer 1

Answer:

Given parabola y=x2    ...(1)

Straight line y=2x−4      ....(2)

From (1) and (2), x2−2x+4=0

Let f(x)=x2−2x+4

∴f′(x)=2x−2

For least distance, f′(x)=0⇒2x−2=0⇒x=1

From y=x2,y=1

So the point least distance from the line is (1,1).

Answer 2

Answer:

The point least distance from the line is (1,1).

Step-by-step explanation:

Given: A straight line is normal to both the parabola$y^2=x\ and\ x^2=y$

To find: The distance of the origin

Solution:

Given parabola $y=x^{2}------1$

Straight line $y=2x-4------2$

From (1) and (2),

$x^{2} -2x+4=0$

Let $f(x)=x^{2}-2x+4$

∴$f^{'} (x)=2x-2$

For least distance,

$f^{'} (x)=0\\2x-2=0\\x=1$

From $y=x^2$ ,y=1

So the point least distance from the line is (1,1).