Differential Equations
Circle from DE Solution
nta_pyq_2024_apr
Grade 12
Question:
Suppose the solution of the differential equation $\dfrac{dy}{dx}=\dfrac{(2+\alpha)x-\beta y+2}{\beta x-2\alpha y-(\beta\gamma-4\alpha)}$ represents a circle passing through origin. Then the radius of this circle is:
2
$\sqrt{17}$
$\dfrac{1}{2}$
$\dfrac{\sqrt{17}}{2}$
Step-by-Step Solution
Key Concept: For the DE to represent a circle, $\beta=0$ and coefficients of $x^2$ and $y^2$ must be equal. From solution: $\alpha=2$, circle $x^2+y^2+x-4y=0$.
$r=\sqrt{1/4+4}=\sqrt{17}/2$.
Correct Answer: 4