What kind of curve is the polar coordinate r = a (cosx + SiNx) x?

R = root (x ^ 2 + y ^ 2)
Cosz = x / radical (x ^ 2 + y ^ 2), Sinz = Y / radical (x ^ 2 + y ^ 2)
So the curve is
Root (x ^ 2 + y ^ 2) = a (x + y) / root (x ^ 2 + y ^ 2)
x^2+y^2=ax+ay
(x-a/2)^2+(y-a/2)^2=a^2/2
So the curve represents a circle

To solve the problem of polar coordinate equation: the center distance of two circles from P = SiNx to P = cosx is?

Polar coordinate derivation of conic curve
How to deduce ρ / ρ cos θ + P = e → ρ = EP / 1-ecos θ

ρ/(ρcosθ+p)=e→ρ=(ρcosθ+p)e→ρ=eρcosθ+ep→ρ-eρcosθ=ep→ρ(1--ecosθ)=ep→ρ=ep/(1-ecosθ)

In polar coordinates, the chord length of the intersection of the line P sin a = root 2 / 2 and the circle P = 2cos a?

Change to rectangular coordinate system first
Straight line: y = root 2 / 2
Circle: (x-1) 2 + y2 = 1
Chord length is root 2

One ant P starts from point B and moves to the left at a speed of 6 units per second, while the other electronic ant Q just starts from point a,

This problem is very simple, let two ants meet after moving х seconds, then there is an equation: 6 х + 4 х = 120 (120 is the distance between a and B, that is, the total distance of two ants moving), and the solution is х = 12, that is, two ants meet in 12 seconds, so the displacement of P is 72 and the displacement of Q is 48 in 12 seconds. So the corresponding number of C on the number axis is 48-20 = 100-72 = 28

At present, one electronic ant P starts from point B and moves to the left at the speed of 6 units / s, while the other electronic ant P moves to the left at the same time
If the electronic ant P starts from point B and moves to the left at the speed of 6 unit length / s, and the other electronic ant Q starts from point a and moves to the left at the speed of 4 unit length / s, let two electronic ants meet at point D on the number axis, do you know the number of point d? (the number of point a is - 20, and the number of point B is 100)

A. The difference between B and Q is 120 units, but P and Q meet at last
Let 6x-4x = 100 - (- 20)
2X = 120, x = 60
The coordinate of point D is (because it moves to the left)
-20+（-4x60）=-260

There are three points a, B, C, AC = 60cm in the line L. an electronic ant moves from point C to point a with a speed of 1cm / S. (1) when a goes to the midpoint of BC, find the distance between a and B; (2) how long does it take for a to walk from midpoint D of BC to midpoint e of AB? (3) when a returns from midpoint e of AB, another electronic ant moves from point C to point a with a speed of 2cm / s, Two ants meet at b5cm away from the point, and calculate the length ab
There is no lack of conditions. I suggest drawing. I'm level one and I can't pass it on.

In the first question, because the distance from point d to point B and point C in BC is equal, so Da + DB = Da + DC = AC = 60cm. In the second question, similar to the above, DB + EB = 1 / 2 (BC + AB) = 1 / 2Ac = 30cm, so the time used is: 30 / 1 = 30s. In the third question, because the second ant is fast, so in a

It is known that a, B and C are the three moving points on the number axis, and the velocities are a unit / s and a unit / s respectively
B units / s and C units / s, and the square of absolute value 5-a + (B-3) + (1-C) to the fourth power = 0
(1) Find the velocity of a, B and C;
(2) If two points a and B start from the origin and move in the positive direction of the number axis respectively, and C starts from the point representing + 20 and moves in the negative direction of the number axis at the same time, a few seconds later, AC = 2BC?
(3) As shown in the figure, if one end of a 16cm long ruler is always coincident with C (the other end D is on the right side of C), and m and N are the midpoint of OD and OC respectively, during the movement of point C, ask: does the value of Mn change? If it changes, find out its value range; if it does not change, ask for its value
Figure of question 3:
——————┳————┳————┳┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼—┳————
1234578910111213141516
O N C M D
(n is the midpoint of OC) (M is the midpoint of OD)

∫|5-a | + (B-3) & sup2; + (1-C) ^ 4 = 0 | 5-a | ≥ 0 (B-3) & sup2; ≥ 0 (1-C) ^ 4 ≥ 0 ∫ a = 5 B = 3 C = 1 VA = 5 VB = 3 VC = 1 (2) T seconds, AC = 2BC T seconds, OA = 5T ob = 3T 0C = 20-t AC = oc-oa = 20-t-5t = 20-6t [BC] = [oc-ob] = [20-t-3t] AC = 2 (BC) 20-6

The number represented by point a on the number axis is one. It moves five units of length to the right to point B, and then point B moves six units of length to the left···
The number represented by point a on the number axis is one. It moves five unit lengths to the right to point B, then moves six unit lengths to the left to point B, and finally to point C to find the rational number represented by point C. for the above results, can you use the mathematical formula? Give it a try

-1+5-6=-2.
The rational number represented by point C is - 2

As shown in the figure, there are three points on the number axis. ABC answers the following questions
(1) What is the number represented by moving point B six units to the right?
(2) After moving point C six units to the left, which of the three points represents the largest number?
(3) How to move two points in ABC so that the number represented by three points is the same?
A=-2 B=-1 C=2

(1) What is the number represented by moving point B six units to the right?
So the coordinate of B is + 6, that is, 6-1 = 5
So the number B represents is 5
(2) After moving point C six units to the left, which of the three points represents the largest number?
So the coordinate of C - 6 is 2 - 6 = - 4
So B is the largest number
(3) How to move two points in ABC so that the number represented by three points is the same?
There are three ways to move
① Move a and B so that they coincide with C. move a 4 units to the right and B 3 units to the right,
② Move B and C so that they coincide with A. move B one unit to the left and C four units to the left
③ Move a and C so that they coincide with B. move a one unit to the right and C three units first

What kind of curve is the polar coordinate r = a (cosx + SiNx) x?