TS EAMCET · Maths · Differential Equations
If \(\alpha\) and \(\beta\) are respectively the order and degree of the differential equation for which \(a x^2+b y^2=1\) is the general solution, then the eccentricity of the ellipse \(\alpha x^2+\beta y^2=1\) is
- A \(\frac{1}{\sqrt{2}}\)
- B \(\frac{1}{2}\)
- C \(\frac{1}{2 \sqrt{2}}\)
- D \(\frac{1}{\sqrt{2}+1}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
Given the solution, \(a x^2+b y^2=1\) \(\ldots\) (i) Now differentiating Eq. (i) w.r.t. \(x\), we get \(2 a x+2 b y \frac{d y}{d x}=0 \text { or } \frac{y}{x}\left(\frac{d y}{d x}\right)=-\frac{a}{b}\) Again differentiating w.r.t. \(x\), we get…
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