Question:
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b: \(\frac{x}{a}+\frac{y}{b}=1\)
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b: \(\frac{x}{a}+\frac{y}{b}=1\)
Updated On: Oct 3, 2023
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Solution and Explanation
\(\frac{x}{a}+\frac{y}{b}=1\)
Differentiating both sides of the given equation with respect to x, we get:
\(\frac{1}{a}+\frac{1}{b}\frac{dy}{dx}=0\)
\(\frac{1}{a}+\frac{1}{b}y=0\)
Again, differentiating both sides with respect to x, we get:
\(0+\frac{1}{b}y=0\)
\(\frac{1}{b}y=0\)
\(y=0\)
Hence,the required differential equation of the given curve is y=0.
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