Question

Question 8(Multiple Choice Worth 1 points)

(07.04 HC)
Right triangle ABC is located at A (-1, 4), B (-1, 1), and C (-5, 1) on a coordinate plane. What is the equation of a circle A with radius AC?
O(x + 1)2 + (y - 4)2 = 9
(x + 5)2 + y - 1)2 = 25
(x + 5)2 + (y - 1)2 = 16
(x + 1)2 + (y - 4)2 = 25

Answer 1

(d) (x + 1)^2 + (y - 4)^2 = 25

Explanation:

The equation of a circle with center (h, k) and radius r is ...

(x -h)² +(y -k)² = r²

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Circle A has its center at point A, so the left side of this equation will look like ...

(x -(-1))² +(y -4)² = r² . . . . . . using (h, k) = (-1, 4)

where r is the length of segment AC. One way to find the value of r² is to use point C for (x, y):

(-5 +1)² +(1 -4)² = r²

16 +9 = r² = 25

Then the equation of the circle is ...

(x +1)² +(y -4)² = 25