The vertices of △XYZ are X(4, 5), Y(4, 13), and Z(8, 9). Find an equation of the circle circumscribed about △XYZ.

An equation is ???

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The equation of the circle is (x - 4)² + (y - 9)² = 4²

Explanation:

The center radius form of the equation of the circle is (x - h)² + (y - k)² = r²

Therefore, given the coordinates of the vertices of the inscribed triangle, we have points on the circumference includes;

X(4, 5), Y(4, 13), Z(8, 9)

Hence, we have;

(4 - h)² + (5 - k)² = r² = h²- 8·h - 10·k + k² + 41(1)

(4 - h)² + (13 - k)² = r² = h² - 8·h + k² - 26·k +185(2)

(8 - h)² + (9 - k)² = r² = h² - 16·h -18·k + k² +145(3)

Subtracting equation (1) from (2), we have;

-(16·k -144) = 0

∴ 16 k = 144

k = 9

Subtracting equation (1) from (3), we have;

-(8·h + 8·k - 104) = 0

Which gives;

8·h + 8·k - 104 = 0, where k = 9 gives

8·h + 8×9 - 104 = 0

8·h - 32 = 0

h = 32/8 = 4

Plugging in the values of h and k in equation (3), we have;

(8 - 4)² + (9 - 9)² = r²

4² = r²

∴ r = 4

The equation of the circle is (x - 4)² + (y - 9)² = 4².

the answer is option c.

explanation:

recycled water alludes to the water that being utilized again after it already  used for farming purposes.   this kind of water frequently contains pharmaceutical gathering due to the compound compost that is utilized for the plants is consumed into the water.