Example 1:

x=cosa y=sina

u=(cosa+2)/(sina+2)

usina+2u=cosa+2

2u=cosa-usina+2

= radical sign (1+u 2) sin (a+b)+2.

-radical sign (1+U2) < = 2u-2 <; = root sign (1+u 2)

4- radical number 7 < = u < = 4+radical number 7

2

(x-3)^2+y^2=9

x-3=3cosa

Y = sinar

therefore

x=3+cosa

Y = Sina

Example 2:

Given that the parameter equation of straight line L is x=2t, y= 1+4t(t is the parameter), and the polar coordinate equation of circle C is ρ = 2 √ 2sinθ, then the positional relationship between straight line L and circle C.

Answer:

The straight line y= 1+2x, that is 2x-y+ 1=0.

Circle ρ 2 = 2 √ 2psin θ

x？ +y？ =2√2y

Center (0, √2), radius √2

The distance from the center of the circle to the straight line is 1/√ 5.

So straight lines and circles intersect.

Example 3:

It is known that the polar coordinate equation of curve C is ρ=2sinθ, the parameter equation of straight line L is x =-3/5t+2, and y = 4/5t-t is the parameter (let the intersection of straight line L and X axis be m and n be the fixed point on curve C, then the maximum value of │MN is? │

Answer:

The parametric equation of the straight line L is transformed into a rectangular coordinate equation,

Get y=-4/3(x-2), let y=0, get x=2,

The coordinate of the point M is (2,0), the curve C is a circle, the center coordinate of the circle C is (0, 1), and the radius r= 1.

Then |MC|= root number 5

So |MN| is less than or equal to |MC|+r= radical number 5+ 1,

So the maximum value of the final result | MN| is (root number 5+ 1).

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