## Question

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.

### Solution

*x*^{2} + *y*^{2} – 12*x* – 10*y* + 52 = 0

Given, AC = 2 units

and A ≡ (2, 2), B ≡ (6, 5)

Hence equation of required circle with centre at (6, 5) and radius 3 is

(*x* – 6)^{2} + (*y* – 5)^{2} = 3^{2}

or *x*^{2} + *y*^{2} – 12*x* – 10*y* + 52 = 0

#### SIMILAR QUESTIONS

Find the equation of the circle the end points of whose diameter are the centers of the circle.

*x*^{2} + *y*^{2} + 6*x* – 14*y* = 1 and *x*^{2} + *y*^{2} – 4*x* + 10*y* = 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 *x*^{2} + 2*ax* – *b*^{2} = 0 and their ordinate are the roots of the equation *x*^{2} + *px* – *q*^{2} = 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 4*x* + *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 5 units touches the coordinates axes in 1^{st} quadrant. If the circle makes one complete roll on *x* axis along positive direction of *x*axis. Find the equation in new position.

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

*x*^{2} + *y*^{2} – 4*x* + 2*y* – 11 = 0