( 1)

P = 4√2 inches (θ+π/4)

=4sinθ+4cosθ

p^2=4psinθ+4pcosθ

Convert to Cartesian Coordinate System

x^2+y^2=4y+4x

(x-2)^2+(y-2)^2=8

C: centered on (2,2), with a radius of 2 √ 2.

x= 1-t

y= 1+t

Line L: x+y-2=0

Distance from the center of the circle (2,2) to the straight line L.

= | 2+2-2 |/√2 =√2 & lt； radius

∴ The straight line L intersects the circle C.

(2)

X+y-2=0 and (X-2) 2+(Y-2) 2 = 8 are simultaneous.

x^2-2x-2=0

|ab|=√( 1+k^2)((x 1+x2)^2-4x 1x2)

? =√(2*(4+8))

? =2√6

The distance from the center (2,2) to the straight line L =√2.

S△ABC= 1/2*2√6*√2=2√3

the second question

( 1)

C 1:p=sinθ-cosθ

p^2=psinθ-pcosθ

Convert to Cartesian Coordinate System

x^2+y^2=y-x

c 1:(x+ 1/2)^2+(y- 1/2)^2= 1/2

C2:

X = sintering cost

Y = Sint+ cost

X+y = 2 points

X-y =-2 cost

(x+y)^2+(x-y)^2=2

C2:x^2+y^2= 1

(2)

Let A be the point on C 1 and B be the point on C2.

Obviously, A and B of the intersecting circle of C 1C2 are the largest at this time |AB|.

AB max=C 1 diameter +C2 radius =√2+ 1.

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