AP EAMCET · Maths · Differential Equations
The differential equation corresponding to the family of circles in the plane touching the \(Y\)-axis at the origin, is
- A \(\frac{d y}{d x}=\frac{y^2-x^2}{2 x y}\)
- B \(\frac{d y}{d x}=\frac{2 x y}{x^2+y^2}\)
- C \(\frac{d y}{d x}=\frac{x^2-y^2}{2 x y}\)
- D \(\frac{d y}{d x}=\frac{x^2+y^2}{2 x y}\)
Answer & Solution
Correct Answer
(A) \(\frac{d y}{d x}=\frac{y^2-x^2}{2 x y}\)
Step-by-step Solution
Detailed explanation
Here, it is given that circle touches the \(y\)-axis at origin. So, equation of family of circles \[ (x-a)^2+y^2=a^2 \] \(\Rightarrow \quad x^2+a^2-2 a x+y^2=a^2\) On differentiating w.r.t. \(x\), we get Now, from Eqs. \((i)\) and (ii), we get…
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