A circle of radius 5 units touches the coordinates axes in 1st quadrant. If the circle makes one complete roll on x axis along positive direction of xaxis. Find the equation in new position.
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
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
Find the equation of the circle the end points of whose diameter are the centers of the circle.
x2 + y2 + 6x – 14y = 1 and x2 + y2 – 4x + 10y = 2
The sides of a square are x = 2, x = 3, y = 1, y = 2 find the equation of the circle drawn on the diagonals the square as its diameter.
The abscissas of two point A and B are the roots of the equation x2 + 2ax – b2 = 0 and their ordinate are the roots of the equation x2 + px – q2 = 0. Find the equation and the radius of the circle with AB as diameter.
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.
Find the equation of circle passing through the three non-collinear points (1, 1), (2, –1) and (3, 2).
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.
Find the equation of circle which touches axis of y at a distance 4 units from the origin and cuts the intercept of 6 units from the axis of x.
Equation of circle in intercepts
Find the equation of the circle which passes through the origin and makes intercepts of length a and b on axis of x and y respectively.
A circle of radius 2 lies in the first quadrant and touches both the axes of coordinate. Find the equation of circle with centre at (6, 5) and touching the above circle externally.
Discus the position of the points (1, 2) and (6, 0) with respect to the circle.
x2 + y2 – 4x + 2y – 11 = 0