The differential equation representing family of circles with centre at point (4, 0) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{dy}{dx}=\frac{4-x}{y}\)
A circle with centre (4, 0) and radius r is
\((x-4)^2 + y^2 = r^2\)
The radius r is the only arbitrary constant. Differentiating with respect to x removes it:
\( \displaystyle 2(x-4) + 2y\frac{dy}{dx} = 0 \)
\( \displaystyle \frac{dy}{dx} = \frac{-(x-4)}{y} = \frac{4-x}{y} \)