JEE Mains · Maths · STD 12 - 9. differential equations
The differential equation representing the family of ellipse having foci either on the \(x-\) axis or on the \(y-\) axis centre at the origin and passing through the point \((0,3)\) is
- A \(xyy' + y^2 - 9 = 0\)
- B \(x + yy'' = 0\)
- C \(xyy'' + x (y')^2 - yy' = 0\)
- D \(xyy' - y^2 + 9 = 0\)
Answer & Solution
Correct Answer
(C) \(xyy'' + x (y')^2 - yy' = 0\)
Step-by-step Solution
Detailed explanation
\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) since. it passes through \((0,3)\) \(\therefore \frac{0}{a^{2}}+\frac{9}{b^{2}}=1\) \(\Rightarrow b^{2}=9\) \(\therefore\) eq. of ellipse becomes: \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{9}=1\) differential w.r.t. \(x,\) we get;…
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