Question

The 'x' co- ordinate of the centre of curvature of the curve xy=1 at the point (1,1) is​

Answer 1

Step-by-step explanation:

x=1

y=1 is the answer of this question

Answer 2

The x- coordinates of the center of curvature is 2 of the curve xy = 1 at the point (1,1).

Given that,

We have to find the x coordinates of the center of curvature of the curve xy = 1 at the point (1,1) is.

We know that,

The curve equation is xy = 1

The point is (1,1)

xy = 1

y = $\frac{1}{x}$

Differentiate with respect to x

$\frac{dy}{dx}= \frac{-1}{x^2}$

One again differentiate with respect to x

$\frac{d^2y}{dx^2}=\frac{2}{x^3}$

Center of curvature coordinates are

X = x - $\frac{y_1(1+y_1^2)}{y_2}$

X = x - $\frac{\frac{-1}{x^2} (1+(\frac{-1}{x^2} )^2)}{\frac{2}{x^3} }$

X = 1 - $\frac{\frac{-1}{1^2} (1+(\frac{-1}{1^2} )^2)}{\frac{2}{1^3} }$

X = 1 - $\frac{-1 (1+1)}{2 }$

X = 1 - $\frac{-2}{2}$

X = 1+1

X = 2

Therefore, The x- coordinates of the center of curvature is 2.

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