A.determine the following equations wether equation of a circle or not.If it is an equationbof a circle ,Write E and if not ,Write N.
1.x²+y²+14x-8y+56=0
2.x²+y²+2x-2y+11=0
3.x²+y²-8y=0
B.write the center-radius form of each circle .
1.Center at origin,radius 6
2.center at (6,1),Radius 7
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A. Determine the following equations whether it is an equation of a circle or not. If it is an equation of a circle, Write E and if not, Write N.
1. x²+y²+14x-8y+56=0 ; E
x² + 14x + 7² + y² - 8y + 4² = -56 + 7² + 4²
(x + 7)² + (y - 4)² = -56 + 49 + 16
(x + 7)² + (y - 4)² = 9
(x + 7)² + (y - 4)² = 3²
C(-7, 4) ; r = 3
The equation is a circle
2. x²+y²+2x-2y+11=0 ; N
x² + 2x + 1² + y² - 2y + 1² = -11 + 1² + 1²
(x + 1)² + (y - 1)² = -11 + 1 + 1
(x + 1)² + (y - 1)² = -9
The equation is NOT a circle because of r² = -9
r should be a positive value for it to be an equation of a circle
3. x²+y²-8y=0 ; E
x² + y² - 8y + 4² = 0 + 4²
x² + (y - 4)² = 16
x² + (y - 4)² = 4²
C(0, 4) ; r = 4
The equation is a circle
B. Write the center-radius form of each circle .
1. Center at origin, radius 6
C(0, 0) ; r = 6
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 0)² = 6²
x² + y² = 36
2. center at (6,1), Radius 7
C(6, 1 ) ; r = 7
(x - h)² + (y - k)² = r²
(x - 6)² + (y - 1)² = 7²
(x - 6)² + (y - 1)² = 49
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