If a variable tangent to the curve $x^2 y=c^3$ makes intercepts $a, b$ on $x$ and $y$ axis respectively, then the value of $a^2 b$ is

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Medium

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Application +4 | -1

If a variable tangent to the curve

x^2 y=c^3

makes intercepts

a, b

x

and

y

axis respectively, then the value of

a^2 b

View answer and explanation

Correct option: C

\frac{27}{4} c^3

Option C (

\frac{27}{4} c^3

) is correct because it is the value of

a^2b

calculated from the given curve equation and tangent properties.

Practice All Chapter MCQs →

f(x)=|x|^{|\tan x|}

f^{\prime}\left(\frac{-\pi}{6}\right)

x

y

x>0

x y=1

x+y

f(x)=[x] \sin (\pi x)

[x]

x

x=k, k

f(x)

y = {\sec ^{ - 1}}\left[ {\mathrm{cosec}x} \right] + \mathrm{cose}{\mathrm{c}^{ - 1}}\left[ {\sec x} \right] + {\sin ^{ - 1}}[\cos x] + {\cos ^{ - 1}}[\sin x],

\frac{{dy}}{{dx}}

\frac{d}{d x} \sin ^{-1}\left(3 x-4 x^{3}\right)

z = y + f\left( v \right),

v = \left( {\frac{x}{y}} \right),

v\frac{{\partial z}}{{\partial x}} + \frac{{\partial z}}{{\partial y}}