The ratio of the distance from the moving point P to the fixed point m and N is 2:1, and | Mn | = 3. The equation of the trajectory of point P is obtained by choosing an appropriate coordinate system Sincerely! Ah, I hope no more people like the one below will come in.

The ratio of the distance from the moving point P to the fixed point m and N is 2:1, and | Mn | = 3. The equation of the trajectory of point P is obtained by choosing an appropriate coordinate system Sincerely! Ah, I hope no more people like the one below will come in.

Let m (x1 Y1) n (N2 Y2)
|PM|:|PN|=2:1
(x-x1)²+(y-y1)²=4[(x-x2)²+(y-y2)²]
Take M as the origin and Mn as the x-axis to establish the coordinate system
|Mn | = 3 points m (3,0) P (x, y)
Let PM = 2pn
x²+y²=4[(x-3)²+y²]
(x-4)²+y²=4

If the generatrix length of a cone is 3 cm and the side area is 6 π cm, the radius of its bottom is 0

Bottom radius = side area ／ bus length ／ π = 6 π ／ 3 ／ π = 2

If the distance difference between the moving point P and the point m (1,0) and the point n (- 1,0) is 2, then the trajectory of the point P is
A two rays B one ray

If the bottom radius of the cone is 3cm and the length of the generatrix is 4cm, then its side area is equal to () a24 π CM & sup2; B12 π CM & sup2; c12cm & sup2; B12 π CM & sup2; c12cm & sup2;

Bottom circumference = 2 π × 3 = 6 π
Side area = 1 / 2 × 6 π × 4 = 12 π
Choose B

The ratio of the distance between the moving point P and the fixed points m (1,0), n (4,1) is 1 / 2, and the equation of the trajectory equation w of P is obtained

With the formula of distance between two points, it can be done

If the radius of the bottom of the cone is 2 cm and the length of the generatrix is 3 cm, the side area of the cone is 2 cm______ cm2．

If the radius of the bottom is 2cm, the perimeter of the bottom is 4 π cm and the side area of the cone is 12 × 4 π × 3 = 6 π cm2

Given that the ratio of the distance from the moving point P to the fixed point (0, - 1) to the distance from the fixed line y = - 9 is 1 / 3, the trajectory equation of the moving point P is obtained

Set point P coordinates (x, y)
[x^2+(y+1)^2]/(y+9)^2=1/9
9x^2+9(y+1)^2=(y+9)^2
9x^2+9y^2+18y+9=y^2+18y+81
9x^2+8y^2=72
x^2/8+y^2/9=1
This is the trajectory equation of the moving point P, which is an ellipse

The height of a cone is 3cm, and the side view is semicircle

(1) Let the radius of the circle on the bottom of the cone be r and the length of the generatrix be L. according to the title, we get 2 π r = 12.2 π L and the solution is L = 2R, so the ratio of the generatrix length to the radius on the bottom of the cone is 2:1; (2) because R2 + 32 = L2, so R2 + 32 = 4r2 and the solution is r = 3, then l = 23, so the total area of the cone is π (3) 2 + 12.2 π· 3.23 = 9 π

Let the distance from the moving point P to f (1,0) be one-third of the distance to the straight line x = 9, and find the trajectory equation of point P?

Let the point be (x, y) and the distance from F to x = 9
[（X-9）/3]^2=(X-1)^2+Y^2
The solution is 8x ^ 2 / 81 + y ^ 2 / 9 = 1

If the bottom radius of the cone is 4cm and the area of the side expanded view is 2 π cm square, then the generatrix length of the cone is --,

It's wrong to estimate the square 2 π of your profile, or it's 12 π. You can take a closer look
Methods: the center angle of the expanded drawing is n and the length of the bus is r
So there is 2 π R * n / 360 = 2 π * 4, that is R * n / 360 = 4
π R & # 178; * n / 360 = 12 π is R & # 178; * n / 360 = 12
The division of the two formulas gives r = 3