 
 
Hello students myself Dr. Gajendra Purohit and today
I will discuss about evolute and before this
I had taught you about envelope
that what is envelope and how we calculate it and
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so please do this and now see what is
evolute. So evolute is locus of the centre
of the curvature is called the evolute of the curve. Right
before this I taught you what is envelope
students so if there is a line
then it's parameter
means if we change the values of the parameter then whatever equations are made
and whatever curves is made then their path
is called envelope . Here evolute is
centre of curvature and for that centre of curvature
the locus is called the evolute
and if I tell you in other words that
whatever are the curves
and whatever is the equation tangent and its normal
the locus of its normal
and the envelope for the normal
that will be
the evolute over here .Right. So I tell
the definition that the locus of the centre of the curvature is called
the evolute of the curve or the evolute of the
curve is a envelope of the normal of the curve
so whatever curve is given and its normal
and the envelope of the normal will be
the evolute. Right. so here the centre of curvature
coordinates are these
so if i talk about a method to calculate the evolute
so the centre of curvature for this
so whatever the centre comes
we will eliminate x and y and after
that the equation that comes  in alpha and beta
we will put x and y so we will have the
equation for the evolute
so here I have made you all understand the method and if you want
to use another method like here it is given y square=4ax
so we can also find evolute by the help of centre of curvature
or with the help of normal equation also
so whatever
is the equation of the normal and its equation
is the evolute so i
will tell you by both the methods and answer will come
same with both the methods so first with the centre of curvature concept
we will solve this
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
so this how we calculate the equation
now I will tell you the same equation with a different method
that how envelope normal
is calculated and for this equation
the parabola normal envelope
that will be the evolute. Right. so that
i will tell you in order to find the answer. so students here the envelope
evolute calculation second method is
 
 
 
 
 
 
the envelope for the normal
that is the evolute. Right. so
we will calculate the envelope and for that the parameter is 'm'
so we need to eliminate 'm'
so students if you don't know how to calculate envelope you can go to the I icon
and find my old video that I uploaded just before this
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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