The circle $x^{2} + y^{2} - 2 x - 2 y + 1 = 0$ is rolled along the positive direction of $x$ -axis and makes one complete roll. Find its equation in new-position.

Open in App

Solution

The given circle is,

$x^{2} + y^{2} - 2 x - 2 y + 1 = 0$

Hence, centre of given circle is $(1, 1)$

and radius $= 1$

$∵$ the rolled is called along the axis of positive direction of

$x$ . When it makes one complete roll, its centre moves horizontally

through a distance equal to its centre mass horizontally through a distance

equal to its circumference $(2 π)$ i,e $2 π$

Thus, the coordination of the centre of the new circle will be. $(1 + 2 π, 1)$

Hence, equation of circle will be,

$(x - 1 - 2 x)^{2} + (y - 1)^{2} = 1$

Suggest Corrections

Similar questions

The circle $x^{2} + y^{2} - 2 x - 2 y + 1 = 0$ is rolled along the positive direction of x-axis and makes one complete roll. Find its equation in es new-position.

Q. The circle

x^{2} - y^{2} - 2 x + 1 = 0

is method angle the positive direction of

x -

axis and makes one complete roll. Find its equation in new position.

Q. A circle of radius

5

units touches the coordinate axes in the first quadrant. If the circle makes one complete roll on x-axis along the positive direction of x-axis, find its equation in new position.

A circle of radius ‘5’ touches the coordinate axes in the first quadrant. If the circle makes one complete roll on x-axis along the positive direction, then its equation in new position is

Q. A circle of radius

14 units

touches the coordinate axes in the first quadrant. If the circle makes three complete rolls along positive direction of

Y - axis

, then the equation of circle in the new position is

Join BYJU'S Learning Program

The circle x2+y2−2x−2y+1=0 is rolled along the positive direction of x -axis and makes one complete roll. Find its equation in new-position.

The circle $x^{2} + y^{2} - 2 x - 2 y + 1 = 0$ is rolled along the positive direction of $x$ -axis and makes one complete roll. Find its equation in new-position.