Question:
The order of the differential equation of all circles passing through the origin and having their centers on the x-axis is
The order of the differential equation of all circles passing through the origin and having their centers on the x-axis is
Show Hint
Order = Number of independent arbitrary constants.
Updated On: May 5, 2026
- 4
- 3
- 2
- 1
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Concept
The order of a differential equation represents the number of independent arbitrary constants in the family of curves.
Step 2: Meaning
A circle with center on the x-axis $(g, 0)$ passing through the origin $(0,0)$ has the equation $(x-g)^2 + y^2 = g^2$.
Step 3: Analysis
Simplifying the equation: $x^2 - 2gx + g^2 + y^2 = g^2 \implies x^2 + y^2 - 2gx = 0$. There is only one arbitrary constant ($g$).
Step 4: Conclusion
Since there is only one independent constant, the resulting differential equation will be of order 1.
Final Answer: (D)
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