CUET · MATHS · PYQ PAPER 2025
The solution of the differential equation \(\frac{d y}{d x}=\frac{a x+c}{b y+d}\) represents a circle when
- A \(a=-b\)
- B \(a=b\)
- C \(a=-2 b\)
- D \(a=3 b\)
Answer & Solution
Correct Answer
(A) \(a=-b\)
Step-by-step Solution
Detailed explanation
\((b y+d) dy = (a x+c) dx\) \(\int (b y+d) dy = \int (a x+c) dx\) \(\frac{b y^2}{2} + d y = \frac{a x^2}{2} + c x + K\) \(a x^2 - b y^2 + 2c x - 2d y + C = 0\) For a circle, coefficients of \(x^2\) and \(y^2\) must be equal: \(a = -b\)
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