Let the distance from the moving point P to the point F (1,0) be 1 / 3 of the distance to the straight line x = 9, find the trajectory equation of the point P, and judge what the trajectory is Be more detailed, thanks!

(X-1)^2+(Y-0)^2=(1/3)^2(X-9)^2
8X^2+9Y^2-72=0

The diameter of the bottom of a cylinder is 4cm and the height is 6cm. What are the surface area and volume of the cylinder and the volume of the cone with the same base and height?

The surface area of this cylinder is [side area plus two bottom areas]
4 divided by 2 equals 2 [cm]
4 times 3.14 times 6 equals 75.36 [square centimeter]
2 times 2 times 3.14 times 2 equals 25.12 [square centimeter]
75.36 plus 25.12 is 100.48 [square centimeter]

The ratio of the distance between point P and a certain point F (2,0) and the distance from point P to a certain line x = 8 is 1:2

Let P (x, y)
√[(x-2)²+y²]/|x-8|=1/2
square
4(x²-4x+4+y²)=x²-16x+64
3x²+4y²=48
x²/16+y²/12=1
This is an ellipse

Eager for the origin of the surface area of cone and cylinder, smart man

Surface area of cone = side area of cone + area of bottom circle
Side area of cone = π RL
Total area of cone = π RL + π R ^ 2
R is the radius of the circle at the bottom of the cone
L is the bus length of the cone
By the way, the generatrix is the radius of the sector after the side is opened

It is known that the distance from point P to line L: x = 4 is √ 2 times of the distance to point F (2,0). Find the figure of the trajectory equation of point P
It is helpful for the responder to give an accurate answer

P (x, y) then the distance from P to x = 4 = | x-4 | pf ^ 2 = (X-2) ^ 2 + (y-0) ^ 2 | x-4 | = radical 2 * the square of both sides of PF (x-4) ^ 2 = 2 [(X-2) ^ 2 + (y-0) ^ 2] x ^ 2-8x + 16 = 2x ^ 2-8x + 8 + 2Y ^ 2x ^ 2 + 2Y ^ 2 = 8x ^ 2 / 8 + y ^ 2 / 4 = 1 is the ellipse with the center at the origin and the focus at (- 2,0), (2,0)

The circumference of the bottom surface of a cone is 18.84 cm. After cutting it in half along the height from the apex of the cone, the sum of its surface area increases by 24 square cm. The volume of the original cone is calculated

Radius of cone: 18.84 △ 3.14 △ 2 = 3 (CM), diameter: 3 × 2 = 6 (CM), height of cone: 24 △ 2 △ 6 △ 12, = 2 △ 12, = 4 (CM); volume of cone: 13 × 3.14 × 32 × 4, = 3.14 × 3 × 4, = 37.68 (cm3); answer: volume of original cone is 37.68 cm3

The ratio of the distance from a moving point P to a certain point Q (2,0) and its distance to a certain line is 1:2?

Conic definition: the ratio of the distance to a fixed point and the distance to a fixed line e is constant
When 0

The perimeter of the bottom surface of a cone is 15.7 cm, and the height is 6 cm. Cut it in half from the top of the cone along the height. How many square centimeters does the sum of the surface area increase compared with the original surface area of the cone?

If the diameter of the bottom surface of the cone is 15.7 △ 3.14 = 5 (CM), the surface area after cutting is increased by 5 × 6 △ 2 × 2 = 30 (square cm); a: the sum of the surface areas is increased by 30 square cm

The distance from the moving point P to the fixed point F (2,0) is greater than that to the straight line x + 1 = 0
The distance from the moving point P to the fixed point F (2,0) is greater than that to the straight line x + 1 = 0 by 1, (1) the equation of the trajectory e of the point P, (2) the vector of the intersection curve e of the straight line passing through the point F at two points a and B

Plot P perpendicular to (1. Y1) point P (x.y)
PF-PA=1
Pf = under root sign (X-2) ^ 2 + y ^ 2
PA=x-1
[under the root sign (X-2) ^ 2 + y ^ 2] - x + 1 = 1

The perimeter of the bottom surface of a cone is 15.7 cm, and the height is 6 cm. Cut it in half from the top of the cone along the height. How many square centimeters does the sum of the surface area increase compared with the original surface area of the cone?

Let the distance from the moving point P to the point F (1,0) be 1 / 3 of the distance to the straight line x = 9, find the trajectory equation of the point P, and judge what the trajectory is Be more detailed, thanks!