Question

A circle of radius 5 units touches the co-ordinates axes in first quadrant. If the circle makes one complete roll on x-axis along the positive direction of x-axis, find its equation in the new position.

Solution

Correct option is

None of these

 

Let C be the centre of the circle in its initial position and D be its centre in the new position.

Since the circle touches the co-ordinates axes in first quadrant and the radius of circle be 5 units.

∴                 Centre of circle is (5, 5)

 

Moving length of circle = circumference of the circle

                                      = 2πr = 2π (5) = 10π  

Now centre of circle in new position is (5 + 10π, 5) and radius is 5 units, therefore, its equation will be

                     (x – 5 – 10π)2 + (y – 5)2 = 52

or       x2 + y2 – 10(1 + 2π)x – 10y + 100π2 + 100π + 25 = 0

                                                           

SIMILAR QUESTIONS

Q1

The abscissa of two points A and B are the roots of the equation x2 + 2ax – b2 = 0 and their ordinates are the roots of the equation x2 + 2px –q2 = 0. Find the equation and the radius of the circle with AB as diameter.

Q2

Find the equation of the circle which passes through the points (4, 1), (6, 5) and has its centre on the line 4x + y = 16.

Q3

Find the equation of the circle passing through the three non-collinear points (1, 1), (2, –1) and (3, 2).

Q4

Show that the four points (1, 0), (2, –7), (8, 1) and (9, –6) are concyclic.

Q5

Find the equation of the circle whose diameter is the line joining the points (–4, 3) and (12, –1). Find also the intercept made by it on y-axis.

Q6

Find the equation of the circle which touches the axis of y at a distance of 4 units from the origin and cuts the intercept of 6 units from the axis of x.

Q7

Find the equation of the circle which passes through the origin and makes intercepts of length a and b on the x and y axes respectively.

Q8

Find the equation of the circle which touches the axes and whose centre lies on the line x – 2y = 3.

Q9

A circle of radius 2 lies in the first quadrant and touches both the axes of co-ordinates. Find the equation of the circle with centre at (6, 5) and touching the above circle externally.

Q10

 

Discuss the position of the points (1, 2) and (6, 0) with respect to the circle

                          x2 + y2 – 4x +2y – 11 = 0.