Let F be the family of ellipse whose centre is the origin and major axis is the y-axis. Then the differential equation of family F isA. `(d^(2)y)/(dx^(2))+(dy)/(dx)(x(dy)/(dx)-y)=0`B. `xy(d^(2)y)/(dx^(2))-(dy)/(dx)(x(dy)/(dx)-y)=0`C. `xy(d^(2)y)/(dx^(2))+(dy)/(dx)(x(dy)/(dx)-y)=0`D. `(d^(2)y)/(dx^(2))-(dy)/(dx)(x(dy)/(dx)-y)=0`

Let F be the family of ellipse whose centre is the origin and major ax

1.	Let F be the family of ellipse whose centre is the origin and major axis is the y-axis. Then the differential equation of family F isA. `(d^(2)y)/(dx^(2))+(dy)/(dx)(x(dy)/(dx)-y)=0`B. `xy(d^(2)y)/(dx^(2))-(dy)/(dx)(x(dy)/(dx)-y)=0`C. `xy(d^(2)y)/(dx^(2))+(dy)/(dx)(x(dy)/(dx)-y)=0`D. `(d^(2)y)/(dx^(2))-(dy)/(dx)(x(dy)/(dx)-y)=0`
Answer» Correct Answer - A Let the equation of the family F of required ellipses be `Ax^(2)+By^(2)=1" …(i)"` It is a two parameter family of curves. Differentiating (i) with respect to x, we get `ax+Byy_(1)=0" …(ii)"` Differentiating (ii) with respect to x, we get `A+By_(1)^(2)+Byy_(2)=0" ...(iii)"` Multiplying (iii) by x and subtracting from (ii), we get `B[yy_(1)-xy_(1)^(2)-xyy_(2)]=0` `rArr" "xyy_(2)+y_(1)(xy_(1)-y)=0rArrxy(d^(2)y)/(dx^(2))+(dy)/(dx)(x(dy)/(dx)-y)=0` This is the required differential equation.

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