Practicing Success
Practicing Success
CUET Preparation Today
| What is the differential equation of the family of circles having centre on y axis and radius 3 units.? |
$(x^2-5)(y')^2+x^2=0$ $(x^2-9)(y')^2+x^2=0$ $(x^2-9)(y')+x^2=0$ $(x^2-9)(y'')^2+x^2=0$ |
| $(x^2-9)(y')^2+x^2=0$ |
| Let us assume the centre of the circle having centre on Y axis be $(0,a)$. Then the equation of the circle is $x^2+(y-a)^2=3^2=9$. Differentiating this equation w.r.to x in both sides we get $2x+2(y-a)y'=0$ So $y-a=\frac{-x}{y'}$ Substituing this in the equation of circle we get $x^2+(-x/y')^2=9$. Solving this the required differential equation is $(x^2-9)(y')^2+x^2=0$ |
