Form the differential equation of all circles which pass through the origin and whose centres lie on the X-axi

Miscellaneous Exercise 6(II) · Q126

Q. Form the differential equation of all circles which pass through the origin and whose centres lie on the X-axis.

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Circles through the origin with centres on the X-axis: $(x-h)^2+y^2=h^2$ (radius $=|h|$ , one constant), i.e. $x^2+y^2=2hx$ . Differentiate: $2x+2y\dfrac{dy}{dx}=2h\Rightarrow h=x+y\dfrac{dy}{dx}$ . Substitute back: $x^2+y^2=2x\left(x+y\dfrac{dy}{dx} …

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Q.Form the differential equation of all circles which pass through the origin and whose centres lie on the X-axis.

Concept understanding — Formation of a Differential Equation whose General Solution is Given

Q.Form the differential equation of all circles which pass through the origin and whose centres lie on the X-axis.

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