A curve passes through the point (3,2) for wh | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the point of contact be $(x_1, y_1)$. The equation of the tangent at $(x_1, y_1)$ is $y - y_1 = m(x - x_1)$,where $m = \frac{dy}{dx}$.Since th

Vedclass · Accepted Answer

$xy=6$

Vedclass · Answer

(C) Let the point of contact be $(x_1, y_1)$. The equation of the tangent at $(x_1, y_1)$ is $y - y_1 = m(x - x_1)$,where $m = \frac{dy}{dx}$.Since the segment of the tangent between the coordinate axes is bisected at $(x_1, y_1)$,the points where the tangent meets the axes are $(2x_1, 0)$ and $(0, 2y_1)$.The slope of the tangent is $m = \frac{2y_1 - 0}{0 - 2x_1} = -\frac{y_1}{x_1}$.Thus,$\frac{dy}{dx} = -\frac{y}{x}$.Separating variables,we get $\frac{dy}{y} = -\frac{dx}{x}$.Integrating both sides,$\ln y = -\ln x + C_0$,which implies $\ln(xy) = C_0$,or $xy = C$.Since the curve passes through $(3, 2)$,we have $3 	imes 2 = C$,so $C = 6$.Therefore,the equation of the curve is $xy = 6$.

$A$ curve passes through the point $(3,2)$ for which the segment of the tangent line contained between the coordinate axes is bisected at the point of contact. The equation of the curve is

Similar Questions

Any curve passes through the point $(3, -4)$. If the slope of the tangent to the curve at any point $(x, y)$ is $\frac{2y}{x}$,then the equation of the curve is . . . . . . .

If the surrounding air is kept at $25^{\circ} C$ and a body cools from $80^{\circ} C$ to $50^{\circ} C$ in $30 \text{ minutes}$,then the temperature of the body after one hour will be

An ice ball melts at a rate proportional to the amount of ice present at that instant. Half the quantity of ice melts in $20 \text{ minutes}$. Let $x_0$ be the initial quantity of ice. If after $40 \text{ minutes}$ the amount of ice left is $Kx_0$,then $K=$

$A$ body is heated to $110^{\circ} C$ and placed in air at $10^{\circ} C$. After $1$ hour,its temperature is $60^{\circ} C$. The additional time required for it to cool to $30^{\circ} C$ is

$A$ normal is drawn at a point $P(x, y)$ of a curve $y=f(x)$. The normal meets the $X$-axis at $Q$. If the length $l(PQ) = k$,where $k$ is a constant,find the equation of the curve passing through $(0, k)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module