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09 Guangzhou No.1 Middle School Mathematics 14 Question Process
Help you solve it ... Be sure to learn the polar coordinate system well, it is the simplest choice! ! ! ! Absolutely need the least time!

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. ..