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Find the curve for which the length of n...

Find the curve for which the length of normal is equal to the radius vector.

Text Solution

Verified by Experts

The correct Answer is:
`y^(2)+-x^(2)=c`
Length of normal `=ysqrt(1+((dy)/(dx))^(2))` and radius vector `=sqrt(x^(2)+y^(2))`
`therefore y^(2)[1+((dy)/(dx))^(2)]=x^(2)+y^(2)`
or `y(dy)/(dx) =+-x`
or `ydy+-xdx=0` or `y^(2)+-x^(2)=c`
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