Question

The order of the differential equation of the family of parabolas whose length of latus rectum is fixed and axis is the X-axis

• A. $2$
• B. $1$
• C. $3$
• D. $4$

Answer 1

The correct option is A $2$

$\begin{array}{c}Equationcanbe{\left(y-k\right)}^2=a\left(x-h\right)a=fixed\\ differentiatingthisweget\\ 2\left(y-k\right).y^{\prime }=ax\\ \left(y-k\right).y^n+y{}^{\prime 2}=\frac{a}{2}\\ \frac{ax}{2y^{\prime }}.y^{\prime \prime }+y{}^{\prime 2}=\frac{a}{2}\\ ax.y^n+2y{}^{\prime 3}=a{y}^{\prime }\\ \therefore order=2\\ Hence,theoptionAisthecorrectanswer.\end{array}$