First of all, remember the basic formula: X = PCOSθY = PSINθx? +Y？ =P？ .
Cleaning:
PSIN(θ+π/4)= P(sinθ* cosπ/4+cosθ* sinπ/4)=√2/2 * psinθ+√2/2 * PCOSθ
=√2/2(X+Y)=2
= & gtx+Y = 2√2 = & gt； X+Y-2√2=0
P=4 = >p？ = 16 = >x？ +Y？ = 16 center (0,0), radius R=4.
Distance from center to straight line: d = |-2 √ 2 |/√ (1+1) = 2.
Let the chord length be l, and according to the vertical diameter theorem: (L/2)? =R？ -Dee? =4? -2? = 16-4= 12
= & gtL=4√3
The answer is 4√3.
If you are skilled, you can choose the polar coordinate system within 1 minute, which is worthwhile, at least much faster than inequality. ..
PS: I'm exhausted .. Mathematical symbols are really hard to type. ..