Question

4

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A circle is centered at the point (5, -4) and passes through the point (-3, 2).
)² + (y +
)² =
The equation of this circle is (x +
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Answer 1

The equation of the circle with center (5, -4) passing through (-3, 2) is (x - 5)² + (y + 4)² = 100.

Step-by-step explanation:

The student is asking for the equation of a circle. We need to use the formula (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

To find r, we calculate the distance between the center (5, -4) and a point on the circle (-3, 2). Applying the distance formula, we get:

√((-3 - 5)² + (2 - (-4))²) = √((-8)² + (6)²) = √(64 + 36) = √100 = 10.

Thus, the radius of the circle is 10, and the equation is (x - 5)² + (y + 4)² = 10².

Simplifying, we get (x - 5)² + (y + 4)² = 100.