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What is the equation of a circle that has a center at (4,-9) and an endpoint at (3,2)

User Rotimi
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Answer:To find the equation of a circle, we need the center coordinates and the radius of the circle. In this case, we are given the center at (4, -9) and an endpoint at (3, 2).

To find the radius, we can use the distance formula between the center and the endpoint. The distance formula is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the given values, we have:

d = sqrt((3 - 4)^2 + (2 - (-9))^2)

= sqrt((-1)^2 + (11)^2)

= sqrt(1 + 121)

= sqrt(122)

So, the radius of the circle is sqrt(122).

Now, we can write the equation of the circle using the standard form:

(x - h)^2 + (y - k)^2 = r^2

Where (h, k) represents the coordinates of the center, and r represents the radius.

Substituting the values, we have:

(x - 4)^2 + (y - (-9))^2 = (sqrt(122))^2

(x - 4)^2 + (y + 9)^2 = 122

Therefore, the equation of the circle with a center at (4, -9) and an endpoint at (3, 2) is (x - 4)^2 + (y + 9)^2 = 122.

Explanation:

User Newtt
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