The family of curves in which the sub tangent at any point of a curve is double the abscissa, is given by a. `x=C y^2` b. `y=C x^2` c. `x^2=C y^2` d. `y=C x`

Explanation

correct answer is A


Suntangent` =frac{y}{m}=frac{y}{frac{dy}{dx}}=2 x `

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Rightarrow frac{2 {dy}}{y}=frac{dx}{x} Rightarrow 2 log y=log x+log c`

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Rightarrow log y^{2}=log cx Rightarrow y^{2}=ck`

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Rightarrow x=cy^{2}`

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