The subnormal at any point of a curve is of constant length '8'. Then the differential equation of the family of curves is

\frac{d y}{d x} = 8 y

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(\frac{d y}{d x}) = \frac{8}{y}

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y . \sqrt{1 + (\frac{d y}{d x})} = 8

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y . \sqrt{1 + {(\frac{d y}{d x})}^{2}} = 8......

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Solution

The correct option is B $(\frac{d y}{d x}) = \frac{8}{y}$
Given that,

The length of subnormal of any curve is $8$ .

We know that the length of subnormal

$= ∣ ∣ ∣ y \frac{d y}{d x} ∣ ∣ ∣$

Therefore,

$∣ ∣ ∣ y \frac{d y}{d x} ∣ ∣ ∣ = 8$

$\frac{d y}{d x} = \frac{8}{y}$

Hence, this is the equation of given curve.

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The subnormal at any point of a curve is of constant length '8'. Then the differential equation of the family of curves is

The correct option is B (dydx)=8yGiven that, The length of subnormal of any curve is 8. We know that the length of subnormal =∣∣∣ydydx∣∣∣ Therefore, ∣∣∣ydydx∣∣∣=8 dydx=8y Hence, this is the equation of given curve.