Equation of circle is

Applying completing the square method

Comparing the above equation with we get center as (-3,3) and radius as .

As centre of the circlre lies on diameter , it will satisfy the equation of diameter, so on putting (-3,3) in equation of diameter we get

=>

=>

Applying the completing the square

Comparing the above equation with we get its center as (-1,-3) and radius (r1)=

Comparing the above equation with we get its center as (2,1) and radius (r2)=

So distance(d) between the centers is units

After applying general formula of length of common chord as and putting the values of r1, r2 and d we get length as

.Circle touches externally if distance between the centers is equal to the sum of the radii .

After applying completing the square, we get

so the center is (-3,-3) and radius is

After applying completing the square

so the center is (6,6) and radius is

Distance between centres and sum of radii are equal.

Hence the circle touches externally.

The equation represents

The above circle can be written as Here the center is (0,0) and radius is also 0 units.

So it is a degenerate circle as degenerate circle is a circle( a point) where radius is zero units.

The equation represents

The general equation of the circle is x2+y2-2gh-2fy+c = 0. Sice the given equations satisfies the general equation, it represents the equation of the circle.

circumcentre of a right angled triangle ABC right angled at A is as circumcentre of right angled triangle lies on the mid pont of the hypotenuse.

so mid point of BC=(,) i.e.(3,2)

(x-a)2 + (y-b)2 = c2 here (a,b) is center and c is the radius

and radius cannot be zero because if radius is zero it will become a point or degenerate circle so c0.

locus of P is a circle with centre at origin and radius .This is known as the director circle of the circle

After completing the square,we get

so center is (4,3) and radius is 4.

Distance between center and given point which is greater than 4.

hence point lies outside the circle .

Since point lies outside of the circle there will be 2 tangents since two tangents can be drawn from external point to a circle.

using distance formulae

on simplifying we get,