Answer:
2) C. (x - 3)² + (y + 2)² = 25
5) x² + y² - 8x - 16y + 54 = 0
6) x² + y² - 10x - 12y + 36 = 0
Step-by-step explanation:
2)
center of circle = 3, -2
x1, y1
end point of circle = 7, 1
x2, y2
the equation of a circle is Pythagorean theorem
x² + y² = r² (where r is the radius of a circle)
distance between points
(x2 - x1)² + (y2 - y1)² = r²
(7 - 3)² + (1 - (-2))² = r²
r² = 25
therefore the equation to the circle is
(x - 3)² + (y + 2)² = 25
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5)
write the general form of a circle with the center (4,8)
and containing the point (-1, 7)
distance between points
(x2 - x1)² + (y2 - y1)² = r²
(-1 - 4)² + (7 - 8)² = r²
r² = 26
(x - 4)² + (y - 8)² = 26
(x - 4)(x - 4) + (y - 8)(y - 8) = 26
x² - 8x + 16 + y² - 16y + 64 -26 = 0
x² + y² - 8x - 16y + 54 = 0
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6)
find the general form of a circle with center (5,6)
and tangent to the y-axis.
center (5,6)
h, k
radius = r²
r = 5
(x - h)² + (y - k)² = r²
(x - r)² + (y - k)² = r²
(x - 5)(x - 5) + (y - 6)(y - 6) = r²
x² - 10x + 25 + y² - 12y + 36 = 25
x² + y² - 10x - 12y + 36 = 0
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