( 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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