AP EAMCET · Maths · Differential Equations
The differential equation of the family of circles passing through \((0,0)\) and having centre on \(X\)-axis is
- A \(2 x y \frac{d y}{d x}+x^2-y^2=0\)
- B \(\left(\frac{d y}{d x}\right)^2+y \frac{d^2 y}{d x^2}+1=0\)
- C \(x y \frac{d y}{d x}+y^2-x^2=0\)
- D \(\frac{d y}{d x}=\frac{x+y}{x-y}\)
Answer & Solution
Correct Answer
(A) \(2 x y \frac{d y}{d x}+x^2-y^2=0\)
Step-by-step Solution
Detailed explanation
Equation of family of circle \((x-r)^2+y^2=r^2\). ...(i) On differentiating w.r.t. \(x\), \(2(x-r)+2 y y^{\prime}=0\) \(\Rightarrow \quad(x-r)+y y^{\prime}=0\) \(\begin{aligned} & \Rightarrow \quad r=x+y y^{\prime} \\ & \text { From Eq. (i), }\end{aligned}\)…
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