The length of the subtangent at any point of the curve $x^{m} y^{n} = a^{m + n}$ is proportional to

Ordinate

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Abscissa

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(O r d i n a t e)^{n}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(A b s c i s s a)^{n}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A Abscissa
$x^{m} y^{n} = a^{m + n}$
Differentiating w.r.t $x$
$x^{m} . n y^{n - 1} \frac{d y}{d x} + y^{n} . m x^{m - 1} = 0$
$\Rightarrow \frac{d y}{d x} = - \frac{m y}{n x} = m^{'}$ (say)
Thus length of sub tangent is $= | \frac{y}{m^{'}} | = \frac{n x}{m}$ , which is proportional to Absccisa

Suggest Corrections

Similar questions

x^{m} y^{n} = a^{m + n}

x^{m} y^{n} = a^{m + n}

y = b e^{- \frac{a}{x}}

The sub-tangent at any point of the curve $x^{m} y^{n} = a^{m + 1}$ varies as

log y = 25 x

Join BYJU'S Learning Program