Circle

Since the centre and radius of the sphere x + y + z + 2 ux + 2vy + 2wz + d = 0 are (-u, -v, - w) and respectively. So, for the sphere x + y + z + 3x - 4z + 1 = 0, Centre and Radius =

Given circles are
and .
Here,

and
Now,

In

Required equation of circle is

Equation of family of concentric circles to the circle is

which is similar to

Thus, the point lies on the cirlce

The tangent at (1, 7) to the curve is



which is also tangent to the circle

i.e.
, which must have equal roots.
Let and are the roots of the equation.
Then



Point of contact is .

We know that, angle of intersection between two circles is given by

or

Here, centre is A (1,2), and Tangent at B (1,7) is x.l +y.l - 1 (x+ l)-2 (y + 7)-20 = 0 ory = 7 ...(1) Tangent at D (4,-2) is 3x-4y-20 = 0 ...(2) Solving (1) and (2), we get C is (16,7) Area ABCD = 2 (Area of A ABC)