If (8, −9) and (6, −3) are the endpoints of the diameter of a circle, what is the equation of the circle?

(x - 7)² + (y + 6)² = 10

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

The centre is at the midpoint of the endpoints of the diameter.

Using the midpoint formula

[ (8 + 6), (- 9 - 3) ] = (7, - 6) ← coordinates of centre

The radius r is the distance from the centre to either of the endpoints.

Using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (7, - 6) and (x₂, y₂ ) = (6, - 3), then

r =

  =

  = = ⇒ r² = ( )² = 10

Thus equation of circle is

(x - 7)² + (y - (- 6))² = 10, that is

(x - 7)² + (y + 6)² = 10

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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