Solve number 8 please
1 answer:
Answer:
see explanation
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k )² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² - 8x + 8y + 23 = 0
collect the x and y terms together and subtract 23 from both sides
x² - 8x + y² + 8y = - 23
using the method of completing the square
add ( half the coefficient of the x / y terms )² to both sides
x² + 2(- 4)x + 16 + y² + 2(4)y + 16 = - 23 + 16 + 16
(x - 4)² + (y + 4)² = 9 ← in standard form
with centre = (4, - 4 ) and r = = 3
this is shown in graph b
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Answer:
Aidan is 2 miles far from the ending point when he reaches the water station.
Step-by-step explanation:
The locations of the starting point, water station and ending point are (3, 1), (3, 7) and (3, 9), all expressed in miles. First we determine the distances between starting and ending points and between starting point and water station by the Pythagorean Theorem:
From starting point to ending point:
(Eq. 1)
From starting point to water station:
(Eq. 2)
The distance between the water station and the ending point is:
(Eq. 3)
Hence, Aidan is 2 miles far from the ending point when he reaches the water station.