CUET · MATHS · PYQ PAPER 2023
Which of the following differential equation represents the family of circles touching the \(x\)-axis at the origin?
- A \(\left(x^2-y^2\right) d y-2 x y d x=0\)
- B \(\left(x^2+y^2\right) d y+2 x y d x=0\)
- C \(\left(x^2-y^2\right) d x+2 x y d y=0\)
- D \(\left(x^2+y^2\right) d y-2 x y d x=0\)
Answer & Solution
Correct Answer
(A) \(\left(x^2-y^2\right) d y-2 x y d x=0\)
Step-by-step Solution
Detailed explanation
Equation of circle: \( x^2 + (y-a)^2 = a^2 \) Simplifying: \( x^2 + y^2 - 2ay = 0 \) Differentiating w.r.t. \( x \): \( 2x + 2y \frac{dy}{dx} - 2a \frac{dy}{dx} = 0 \) From original equation: \( a = \frac{x^2+y^2}{2y} \) Substitute \( a \):…
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