1. GIVEN THE EQUATION OF THE CIRCLE DETERMINE THE RADIUS AND THE CENTER
a. x² + y² = 1
b. (x - 2)² + (y + 6)²= 20 - 2
c. x² + y² - 8x - 4y + 16 = 0
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1. GIVEN THE EQUATION OF THE CIRCLE DETERMINE THE RADIUS AND THE CENTER
a. x² + y² = 1
b. (x - 2)² + (y + 6)²= 20 - 2
c. x² + y² - 8x - 4y + 16 = 0
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Answer:
The equation of a circle is in form of (x-h)² + (y-k)² = r², with (h,k) being the center of the circle.
Now, the standard equation for a circle with a center on the origin (0,0) is x²+y² = r²
Therefore, The answer for the following are:
1.) x² + y² = 1
The center would be (0,0) and the radius would be √1 which is just 1.
2.) (x-2)² + (y+6)² = 20
The center would be (2,-6) and the radius would be √20 which is 2√5
3.) x² + y² -8x - 4y + 16 = 0
We need this equation first to be in standard equation of a circle (x-h)² + (y-k)² = r²
Simplifying it, we get:
(x-4)² + (y-2)² = 4
Thus, the center would be (4,2) and the radius would be 2.