On the mathematical problems of polar coordinates 1. The polar coordinate equation of a circle with radius a and center C (a, 0) (a > 0) is (P = 2acos θ) 2. The polar coordinate equation of the circle with radius R is (P = R) How are their answers worked out? What are the conditions under which the polar equations are worked out?

On the mathematical problems of polar coordinates 1. The polar coordinate equation of a circle with radius a and center C (a, 0) (a > 0) is (P = 2acos θ) 2. The polar coordinate equation of the circle with radius R is (P = R) How are their answers worked out? What are the conditions under which the polar equations are worked out?

1. In rectangular coordinate system
(x-a)^2+y^2=a^2
==>x^2+y^2=2ax
Let P = root sign (x ^ 2 + y ^ 2), and the angle between any point of the circle and the positive half axis of X is θ
Then x = PCOS θ, y = PSIN θ
The equation can be written as p ^ 2 = 2apcos θ, = = > P = 2acos θ
2. Similar
X ^ 2 + y ^ 2 = R ^ 2, = = > polar coordinates: P = R
The variables in polar coordinates are p and θ