The differential equation of the family of curves for which the length of the normal is equal to a constant k, is given by

Options

A. ` y^(2) ((dy)/(dx))^(2)= k^(2) - y^(2)`
B. `[ y(dy)/(Dx)]^(2)=k^(2)-y^(2)`
C. ` y(dy)/(dx)=k^(2)-y^(2)`
D. `[ y(dy)/(dx)]^(2)=k^(2)+y^(2)`

Answer

a

Explanation

The length of normal is given by ,` y sqrt(1+((dy)/(dx))^(2))`
` :. y sqrt (1+((dy)/(dx))^(2))= k ` [ given ]
` rArr y^(2) [ 1+ ((dy)/(dx))^(2) ] = k^(2) rArr y^(2) + y^(2) ((dy)/(dx))^(2)= k^(2)`
` rArr y^(2) ((dy)/(dx))^(2)= k^(2) - y^(2)`