The differential equation of the family of curves for which the length of the normal is equal to a constant k, is given byA. ` 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)`

The differential equation of the family of curves for which the length

1.	The differential equation of the family of curves for which the length of the normal is equal to a constant k, is given byA. ` 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» Correct Answer - a 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)`

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The differential equation of the family of curves for which the length of the normal is equal to a constant k, is given byA. ` 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)`

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