The curvature of y^2 = 4ax ?
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Answer:
The radius of curvature of a paroba
y2=4ax at the origin 2a
To find the radius of curvature of a paroba y2 = 4ax at the origin
y2=4ax
differentiating both sides
2yy'=4a
Or
y'=2a/y
For (x, y) = (0,0)
y'all = infinity
So we go for alternative formula
hence we differentiate both side
y2=4ax
2y=4ax' ...........eq-n (1)
or
x'=y/2a
At (0,0),x'=0
Differentiating (1) again we get..
1/2a = x''
We know radius of curvature ,
r=(1+x'^2)^3/2/x''
Hence, at (0,0)
r=1+0^3/2/1/2a
= 2a
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Answered by
2
- For , y-axis is tangent at (0, 0), while for , x-axis is tangent at (0, 0). Thus the two curves cut each other at right angles.
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