Given the equation x 2 y 2 4 x 2 y 4 0, then the maximum value of x 2 y 2

x2+y2+4x-2y-4=0, which is: (x+2) 2+(y-1) 2=9, which is a circle, the center of the circle (-2,1), and the radius 3

The maximum value of x 2+y 2 is the maximum distance from the point of the circumference of the circle to the origin of (x+2) 2+(y-1) 2=9.

The distance from the origin to the center of the circle + the radius is the result

x^2+y^2+4x-2y-4=0

x+2)^2+(y-1)^2=9

Let x+2=3cosa

Then (y-1) 2=9-9(cosa) 2=9(sina) 2 Because the range of sina is symmetrical with respect to the origin, you might as well let y-1=3sina so x=3cosa-2, y=3sina+1 so x 2+y 2=9(cosa) 2-12cosa+4+9(sina) 2+6sina +1

9-12cosa+4+6sina+1

6sina-12cosa+14

6 2 + 12 2) * sin(a-arctan12 6)+146 5*sin(a-arctan2)+14 so sin(a-arctan2)=1, the maximum value = 6 5+14

I don't know if you've learned the equation of a circle, but if you do, it's easy to do.

x^2+y^2+4x-2y-4=0 (x+2)^2+(y-1)^2=9 .The expression is a circle with a center of (-2,1) and a radius of 3. x 2+y 2 can be understood as the distance from the point on the circle to the origin of the trousers (0,0) Hu Qing.

The maximum value of x 2+y 2 is [(2) 2+1 2]+3=3+ 5This is because the line that passes through the diameter is the longest. Upstairs did something wrong. Cause.

The maximum value of x-2y is 10Reducing the equation x 2 + y 2-2 x + 4y = 0 into the standard form of the circle is obtained (x-1) 2 + y+2) 2 = 5 ream, x-1 = 5sinty+2 = 5cost, then x-2y = 5sint - 2 5cost + 5= 5(sint -2cost) +5= 5* 5( 5 5sint - 2 5 dust tung 5cost) +5=

Let z(x,y,r) =3x 2+4y 2+(2x 2+2y 2-xy-4)r

Find the partial derivatives for x, y, and r, respectively; Partial derivative of z to x = 6x+4xr-yr ; Partial derivative of z to y =8y+4yr-xr ; z vs. r is a good conductor =2x 2+2y 2-xy-4

System of equations: 6x+4xr-yr=0;8y+4yr-xr=0；2x^2+2y^2-xy-4=0；

x=2 (1 2), y=(2 (1 sun lead2)) 2; x=-2^(1/2),y=-(2^(1/2))/2

x=-(2^(1/2))/2,y=3(2^(1/2))/4; x=(2^(1/2))/2,y=-3(2^(1/2))/4

Then bring in the obtained data residue in turn to find the maximum value.

It is known that it is a circle with (2,0) as the center of the circle, and if you draw the diagram, you can know that 0 is so x 2-y 2=2(x 2-2x)=2(x-1) 2-2

When x = 4, the maximum value is 16

Summary. Dear Hello Glad to serve you x 2+y 2-4x-2y-4=0 then the maximum value of x-y is frac}

x 2 + y 2-4x-2y-4 = 0 then the maximum value of x-y is .

Dear Hello It is a pleasure to serve you, lifting the mountain with only silver x 2+y 2-4x-2y-4=0, then the maximum value of x-y is the positive finger frac}

Hello Fusun hand x 2+y 2-4x-2y-4=0 then the maximum value of x-y is frac} First of all, the equation is matched to a perfectly squared form.

This is the square of a circle with a radius of 3 at the origin of the coordinate system, and we can deform this equation of pure dispersion into: (x-2) 2+(y-1) 2 = 3 2 This is the equation for a circle with a radius of 3 centered on the point (2,1) If we draw this equation in a coordinate system, we know that the two farthest points on the circle are the two points on the circle that are tangent to the line y=x.

The coordinates of the last or acre of these two points are ( frac}, frac}) and ( frac}, frac}), substituting it into x-y, i.e. the maximum value of x-y is frac}

Is there anything that can be solved without a circle?

Yes, yes, you can solve it without a circle.

Can you tell me about it?

Dear Hello, you can use the method of translating the coordinate system to solve the problem of the Huai ruler set x'=x-2 and y'=y-1, then the original equation can be deformed as x 2 + y 2-4x-2y-4 = 0 longrightarrow x'^2+y'2 = 9, which indicates (x',y') constitutes a circle with a radius of 3 at the origin of the circle with the center of the circle.

Yes. So what's the answer?

So the answer is frac}

What about people. Hello The slope of the straight line is calculated to be Zheng Wanmu k= frac=-1, and its mapping point on the straight line y=x is (x 0, y 0) =frac}, frac}).

Finding the distance from (2,1) to (x 0, y 0) gives us the maximum value of x-y, which is frac}. Here the slope of the straight line is negative, so (2,1) is on the top left of (x 0, y 0).

With this in English, I really don't know what the answer is. <>

Dear hello this answer is frac}

Wait a minute, this system comes out like this.

Okay, dear.

x 2 + y 2-4x-2y-4 = 0 then the maximum value of x-y is 3 3 that is to say, the answer is 3 3 pro.

The original form can be simplified and erected.

x+2)^2+(y-1)^2=9

This is the absence of a circle with a radius of (-2,1).

So the maximum value of x 2+y 2 is the maximum distance from the point on the circle to the origin of Yu Xianchun.

is the distance from the center of the circle to the origin plus the radius.

Equal to 3 + root number 5

x^2+y^2-2y=0

x^2+(y-1)^2=1

x=cosa,y=sina+1

x^2+4y

cosa^2+4(sina+1)

1-sina^2+4sina+4

sina-2)^2+9

sina[-1,1]

When sina = 1, f has a maximum value that is bridged: side-by-side.

The maximum value of the so-min stupid x 2+4y is 8