TS EAMCET · Maths · Differential Equations
The differential equation of the family of all circles of radius ' \(a\) ' is
- A \(y_1 y_2+\left(1+y_1^2\right)=a\)
- B \(\left(1+y_1^2\right)^3=a^2 y_2^2\)
- C \(1+y_1^2=y_2^2+a^2\)
- D \(y_2^2+1=y_1^2+a^2\)
Answer & Solution
Correct Answer
(B) \(\left(1+y_1^2\right)^3=a^2 y_2^2\)
Step-by-step Solution
Detailed explanation
\((x - h)^2 + (y - k)^2 = a^2\) \(2(x - h) + 2(y - k)y_1 = 0 \implies (x - h) + (y - k)y_1 = 0\) \(1 + (y - k)y_2 + y_1^2 = 0 \implies (y - k) = -\frac{1 + y_1^2}{y_2}\) \((x - h) = -(y - k)y_1 = \frac{(1 + y_1^2)y_1}{y_2}\)…
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