The length of the subtangent at (2,2) to the curve x5=2 y4 is

Question

The length of the subtangent at (2,2) to the curve x5=2 y4 is (A) (5/2) (B) (8/5) (C) (2/5) (D) (5/8)

Tardigrade Admin · Accepted Answer

Given that, 2 y4=x5 On differentiating w.r.t. x, we get 8 y3 (d y/d x)=5 x4 ⇒ ((d y/d x))(2,2)=(5(2)4/8(2)3)=(5/4) ∴ Length of subtangent =(y/d y / d x) =(2/5 / 4)=(8/5)

Q. The length of the subtangent at $(2, 2)$ to the curve $x^{5} = 2 y^{4}$ is

$\frac{5}{2}$

$\frac{8}{5}$

$\frac{2}{5}$

$\frac{5}{8}$

Given that,
$2 y^{4} = x^{5}$
On differentiating w.r.t. $x$ , we get
$8 y^{3} \frac{d y}{d x} = 5 x^{4}$
$\Rightarrow (\frac{d y}{d x})_{(2, 2)} = \frac{5 ( 2 ) ^{4}}{8 ( 2 ) ^{3}} = \frac{5}{4}$
$∴$ Length of subtangent $= \frac{y}{d y / d x}$
$= \frac{2}{5/4} = \frac{8}{5}$

Q. The length of the subtangent at (2,2) to the curve x5=2y4 is

25​

58​

52​

85​