# 5. Show that the normal at any point  to the curve is at a constant distance from the origin.

We know that the  slope of tangent at any point is given by
Given equations are

We know that

equation of normal with given points and slope

Hence, the equation of normal is
Now perpendicular distance of normal from the origin (0,0) is

Hence, by this, we can say that

the normal at any point  to the curve

is at a constant distance from the origin

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