The families of curves represented by the solution of the equation dydx=−(xy)n
For n=−1 and n=+1, respectively, are
A
Hyperbola and Parabolas
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B
Circles and Hyperbolas
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C
Parabolas and Circles
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D
Hyperbolas and Circles
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Solution
The correct option is D Hyperbolas and Circles dydx=−(xy)n
forn=−1 dydx=−(xy)−1 ∫dyy=−∫dxx lny=−ln(x)+lnk ln(y)+ln(x)=ln(k) ln(xy)=ln(k)
taking log inverse xy=k Rectangular hyperbola
for n=1 dydx=−(xy) ∫y.dy=−∫x.dx y22=−x22+c x2+y2=c circle.
for n=−1; Hyperbolas
for n=+; circles