Equation of the curve passing through the point (1 , 2) such that the intercept on the x -axis cut off between the tangent and origin is twice the abscissa is given by xy=k then find k .

Question

Equation of the curve passing through the point (1 , 2) such that the intercept on the x -axis cut off between the tangent and origin is twice the abscissa is given by xy=k then find k . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

equation of tangent <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-3hphtbhxykmw6w0i.jpg" /> ∵ x-y(d x/d y)=2x displaystyle ∫ (d y/y)=- displaystyle ∫ (d x/x) ⇒ ln(y)+ln(x)=ln(c) ⇒ c=2. ⇒ xy=2.

Q. Equation of the curve passing through the point $(1, 2)$ such that the intercept on the $x$ -axis cut off between the tangent and origin is twice the abscissa is given by $x y = k$ then find $k$ .

equation of tangent

$∵ x - y \frac{d x}{d y} = 2 x$
$\int \frac{d y}{y} = - \int \frac{d x}{x}$
$\Rightarrow l n (y) + l n (x) = l n (c)$
$\Rightarrow c = 2.$
$\Rightarrow x y = 2.$

Q. Equation of the curve passing through the point (1,2) such that the intercept on the x -axis cut off between the tangent and origin is twice the abscissa is given by xy=k then find k .

equation of tangent ∵x−ydydx​=2x ∫ydy​=−∫xdx​ ⇒ln(y)+ln(x)=ln(c) ⇒c=2. ⇒xy=2.

Q. Equation of the curve passing through the point $(1, 2)$ such that the intercept on the $x$ -axis cut off between the tangent and origin is twice the abscissa is given by $x y = k$ then find $k$ .

equation of tangent

$∵ x - y \frac{d x}{d y} = 2 x$
$\int \frac{d y}{y} = - \int \frac{d x}{x}$
$\Rightarrow l n (y) + l n (x) = l n (c)$
$\Rightarrow c = 2.$
$\Rightarrow x y = 2.$