Question

The order and degree of the differential equation of all circle touching the $x-$axis at the origin and centre on the $y-$axis, are respectively

• A. $2,1$
• B. $1,2$
• C. $1,1$
• D. $1,3$

Answer 1

The correct option is B $1,2$

Here center is at $(0,r)$ on Y-axis and radius =r

Equation of the circle :

$\Rightarrow x^2+(y-r{)}^2=r^2$

$\Rightarrow x^2+y^2-2yr=0$

Here there is only one variable 'r' and therefore order =1

Differentiate on both sides

$\Rightarrow 2x+2y{y}^{{}^{\prime }}-2y{y}^{{}^{\prime }}r=0$

$\Rightarrow r=\frac{x+y{y}^{{}^{\prime }}}{y{y}^{{}^{\prime }}}$

Substituting 'r' in the above equation we get a power of 2 in $y^{{}^{\prime }}$

$\Rightarrow$degree =2

$\therefore$ order =1, degree =2