A circle has its center at (-1, 2) and a radius of 3 units. What is the equation of the circle?
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Answer:
Step-by-step explanation:
The standard equation of a circle centered at (a,b) with radius r would be (x - a)^2 + (y - a)^2 = r^2
This example represents a circle with center (2, - 1) having a radius of 3
The parametric equation of a circle centered at (0,0) would be;
x = r cos t,
y = r sin t
And so when centered at (a, b) we would have;
x = a + r cos t,
y = b + r sin t
In this case x = 2 + 3 cos t, and y = - 1 + 3 cos t
Now if the particle starts at (-1, - 1), correspondent to a start parameter of t = π, we need two revolutions so it should be that t = π + 2 * 2π = 5π.
